/sci/ - Science & Math

>>9570309
math =/= science

>>9570309
No, uncertainty is an assumption based on things not being infinite.

>>9570315
You have uncertainty regardles of finiteness being present. For instance, the limiting case of a distribution curves resolution gives no additional insight on how the sampling is perforned.

Infinity is a difficult concept and most cases where it sounds "wrong" thats because you misapply mathematics^^ e.g. your example : you use "=" in a completely other sense than you'd do in "x = 1", in your case it is ( at best, though i dont like this notation and one could argue it is wrong) used to show the sum of an infinite series. Which is way different from any finite sum you could come up with :P

If you come from a scientific background , you could argue "there's a minimal and a maximal time/space/energy... with any physical meaning ( e.g. 10^(-43) s for time)", so you could argue "well a physicist can't talk about anything outside those boundaries, since physics is bounded by our universe", but nothing more than that. What happens most often is a physical value not being clearly enough defined so it "seems" like infinity. E.g. what is the "temperature" of laser light? For some (naive) definitions of temperature this is a hard question.

>>9570343
what is the temperature of laser light

>>9570309
>Is infinity pseudo science?
Math isn't science

>>9570358
>formal science isn't science

I wish mods deleted these stupid threads desu.

>>9570365
>fell for the 300k starting meme
stay mad

>>9570354

depends entirely on your definition of Temperature. You could make a case for nearly anything here^^ If you take electron energy levels or boltzmann inversion here you could talk about a NEGATIVE temperature ( on the kelvin scale) which is actually hotter than say "1K" and depending on your (naive) definition of temperature may as well be hotter than the hottest possible temperature, i.e. "infinite" for some definitions of infinity

>>9570309
Eh. Infinity is an axiom of ZFC. So in a way it's an assumption. But it's an assumption that gives rise to a staggeringly enormous amount of interesting mathematics. It also doesn't lead to any logical contradictions. So there's no problem in taking it as an axiom.

You're welcome to do math without the axiom of infinity but it just won't be as interesting. Nor will it be as useful.

Also if results like 0.999...=1 and 1/2+1/4+1/8+1/16+...=2 are not intuitive to you then you may actually be a retard.

>>9570487
Sorry, I meant 1/2+1/4+1/8+...=1 (not 2).

>>9570309
Why the apeirophobia?

>>9570389
people like you are the reason I took a 7 month hiatus from this board.

>>9570576
fuck off back to >>>/pol/

>>9570309
Infinity has different meanings, all of which are very well defined in mathematics. Real numbers are (often) constructed as the equivalence classes of rational cauchy sequences whose difference converges to 0.

>>9570362
Science is literally empiricism. Math is not. Math is used in science to formulate hypotheses, but math itself is not an empirical investigation.

top 10 worst threads 2018

>>9570924
>top 10 worst threads 2018
Meanwhile the catalog is filled with IQ, racebait and /pol/ threads

>>9571051
Does one even exist? Like count apples. One apple, two apple. No you can't because an apple is an arbitrary measurement. Each apple has different and made of particles. There isn't one apple.

>>9571368
On a human scale, quantity makes sense. What would you suggest as an alternative?

>>9571368
>apples don't exist
the lengths to which you people will go

Infinity is pseudo intelligence.

Its not math, its not science, it's not intelligent.
To do infinite summation is to say you never stop summing, which means you can never acquire a result, which means infinite summation is not useful. If you can acquire a result from it, then there was an end to the summation and thus not actually infinite, unless you redefine infinity from "never ending" to "a greatest, real number value", meaning "infinite" is just a counter-intuitively retarded name for an obviousy finite number. If you then say "no greatest real number exists", then infinity doesn't then exist, which also makes it useless.

Infinity is a paradox, and as a paradox it is not useful.

[math]0.\bar{9 \neq 1[/math] because there can only exist a never ending amount of 9's never approaching anything but more 9's. The result of an infinite sum isn't defineable because you never reach an end result. The amount of 9's in 0.999... cannot be infinite unless "infinite" is used in lieu of "an arbatrarily large real finite number". The result of an infinite sum cannot equate unless "infinite" is used in lieu of "an arbitrary large real finite number". Furthermore, replacing "infinite" with "an arbatrarily large real finite number" then provides for [math]\frac{1}{\infty}>0[/math], meaning for "an arbitrary amount of 9's in 0.999..." would necessitate the addition of [math]\frac{1}{\infty}[/math] to properly sum 1, and "an arbitrary amount of summation" in an infinite sum to finitely equate a real value, and even though none of these steps actually logically worth regardless of definition, it still doesn't provide for any sense to be made about which number infinity is supposed to be.

Only brainlets who have been programmed by math instructors via obedience believe infinity is rigourosly defined or useful. It isn't.

>>9571474
>To do infinite summation is to say you never stop summing, which means you can never acquire a result
You're retarded. No one is sitting down to add each step in a summation algorithm, instead an analytical trick is used to transform that algorithm into something else that can be evaluated in finite steps.

>If you can acquire a result from it, then there was an end to the summation and thus not actually infinite
A finite amount can be divided into infinite parts, and therefore infinite parts can form a finite summation.

You have less understanding of the concept you are trying to criticize than an elementary school student, and treating you lack of basic understanding as a paradox. Dunning Kruger effect in action.

>>9571516
Saying there are an infinite, non-finite amount of parts between finite 1 and finite 2 means you can never reach 2 from 1 by incrementing in those parts.

Really you just projected by invoking dunning krueger when you had no idea what you were talking about but decided to post anyway. Moreover, you're selfish and evil for wasting my and anyone elses time in reading your completely uninformative post. You ultimately didn't even comprehend my post that you replied to and didn't understand the strict definitions offered.

[math]\sum_{n=1}^{\infty} \frac{1}{2^n}[/math] will never equal 1 or approach 1. It wont even technically equal 0.999...

The moment you have a sufficient amount of sequential 9's in the result to be assumed as infinite, you would also have an infinite amount of unordered random numbers after it. Cutting this entire value in have spacially, the left half from middle to the decimal point would be all 9's, but the right half would be random gobbledygook numbers in no defineable pattern, and that is when all possible dogits of the significand have been accounted for and filled, from the 1st decimal place at 0.9, to the infinite'th decimal place.

1/2^n is obviusly less than 2/3^n or 3/4^n, and these are all leas than 9/10^n which would be a true uninterrupted string of 9's.

[math]\sum_{n=1}^{\infty} \frac{1}{2^n}[/math] will never equal 1 or approach 1. It wont even technically equal 0.999...

The moment you have a sufficient amount of sequential 9's in the result to be assumed as infinite, you would also have an infinite amount of unordered random numbers after it. Cutting this entire value in half spacially, the left half from middle to the decimal point would be all 9's, but the right half would be random gobbledygook numbers in no defineable pattern, and that is already when more than all possible digits of the significand have been accounted for and filled, from the 1st decimal place at 0.9, to the infinite'th decimal place. For 1/2^n to properly approach 0.999... would require the total amount of digits be infinite, and only half of all those digits would be 9's so to cut off the latter half and assume 1/2^n = 0.999... is to actually say [math]\sum_{n=1}^{2 × \infty} \frac{1}{2^n}[/math] where after doubling on the infinite amount of summable iterations, there would finally be an infinite amount of 9's, even though it's still further followed by an infinite amount of arbitrary unordered digits of random numbers.

1/2^n is obviusly less than 2/3^n or 3/4^n, and these are all leas than 9/10^n which would be a true uninterrupted string of 9's.

Infinity isnt well defined or useful. Only brainlets pretend it is.

>>9570343
>your example : you use "=" in a completely other sense than you'd do in "x = 1",
Wrong.

>>9571613
>[math]\sum_{n=1}^\infty \frac{1}{2^n}[/math] will never approach 1.

Let's tackle this part of your claim. Note that
[eqn]\sum_{n=1}^k \frac{1}{2^n} = \frac{2^k - 1}{2^k}.[/eqn] We can easily see that this equality holds true for [math]k=1[/math]. Let [math]k\in\mathbb N_0[/math] be arbitrary and assume the equality holds. We show that it also holds for [math]k + 1[/math].
[eqn]\sum_{n=1}^{k+1} \frac{1}{2^n} = \sum_{n=1}^k \frac{1}{2^n} + \frac{1}{2^{k+1}} = \frac{2}{2}\cdot\frac{2^k - 1}{2^k} + \frac{1}{2^{k+1}} = \frac{2^{k+1}-1}{2^{k+1}}.[/eqn]
This proves that the equality holds for any arbitrary natural number greater than or equal to 1 and all that is left to do is show that [math]\frac{2^k - 1}{2^k}[/math] approaches 1.

Let [math]\varepsilon > 0[/math] be arbitrary. By the Archimedian property there exists some [math]k_0 \in \mathbb N_0[/math] such that [math]k_0 > \frac{1}{\varepsilon}[/math]. Let [math]k \in \mathbb N_0[/math] be arbitrary and assume that [math]k \geqslant k_0[/math]. It then follows that [math]2^k > k \geqslant k_0 > \frac{1}{\varepsilon}[/math]. From here it follows that
[eqn]\varepsilon > \frac{1}{2^k} = \left|\frac{-1}{2^k}\right|
= \left|\frac{2^k -1 - 2^k}{2^k}\right|
= \left|\frac{2^k -1}{2^k} - \frac{2^k}{2^k}\right|
= \left|\frac{2^k -1}{2^k} - 1\right|
[/eqn]

This proves that for any arbitrary distance [math]\varepsilon[/math] there is some point after which all the partial sums of the series lie closer than that and as such this proves that the series does approach 1.

>>9571638
this >>9571723 was meant to give you a (you) but you deleted the initial post so here is your (you).

>>9571723
While this is nice, it's rather misguided. In fact, the whole idea that an infinite sum ``approaches'' a number is wrong. An infinite sum is a complete object. It IS a number (assuming convergence). A convergent infinite sum is simply a different way of representing a number. So $\sum_{n=1}^{\infty} \frac{1}{2^n}$ is just a weird way of writing the number 1. Just like 2/2 is another way of writing the number 1.

It's kinda like having a nickname for somebody. You might refer to a friend as `Robert' while I call him 'Bobby'. We're referring to the same person, but in different ways. Same thing with the number 1 and that infinite sum. Different ways of referring to the exact same mathematical object.

>>9571723
If an infinitely large arbitrary number can exist, an infinitely small arnitrary number must then also exist.

If you use these definitions, the opposite of infinity is a value that is the closest to zero but greater than zero. If 0.999... = 1, then 1/infinity = 0.
If 1/infinity = 0, a/b = c
Then 1/0 = infinity, a/c = b.
If 1/infinity = 0, there does not exist an infinitely small real number, and therefore does not exist an infinitely large real number, thus infinity does not exist and neither does an infinite amount, thus this conversation is no longer about "0.999... & 1", because there is no rational, consistent, reliable way of defining what "0.999..." is without invoking infinity which itself is not rationally, consistently, reliably defined. If the concept of infinity cant work, you cant then take a next step by using infinity in any specific manner. Doing so is the equivalent of knowing infinity is unachieably countable but treating infinity+1 as real, as it's next step countable step. Non-finitests don't do this, so non-finitests are stuck forced to abritrarily force finitest rules on infinity without changing the definition of infinity. Infinity+1 doesnt rationalize as the next step after infinity, so using infinity doesn't rationalize as the next step after not defining infinity.

Infinity is a fucking paradox for brainlets. Just stop. Any and every attempt to justify using it is easily proven fallible, so anyone who tries to do it anyway is an idiot.

There is no such thing as getting a result from unending work. There is also no such thing as a largest real number. Infinity = worthless.

>>9571749
Oh I don't disagree, but he was just going to throw retarded retorts that "convergence isn't equality" so I just opted to show that the partial sums definitely do approach 1, which he also denied. And as you said, the entire series is indeed equal to 1.

>>9571770
>If an infinitely large arbitrary number can exist, an infinitely small arnitrary number must then also exist.
It can't exist and nowhere is it claimed to exist in the post you are replying to.

>>9571780
>It can't exist and nowhere is it claimed to exist in the post you are replying to.
Yes, infinity can't exist, thanks for agreeing.

I bet you didn't even realize thats what you typed. I think its time to take a step back and realize this thing called infinity is fully retarded, and trying to justify it just leads to people becoming retarded.

>>9571787
There are no real numbers that are "infinitely large", the same is true for natural numbers. That claim is in no way equivalent to "Infinity can't exist". There is no upper bound to the natural numbers or to the real numbers, which is what we mean when we say there are "infinitely" many. The only thing that is inconsistent here is your usage of the concept infinity.

>>9571791
You can have a number that's arbitrarily large, though, right? Like, something that for the sake of argument is larger than any given value, but can still be treated as a real number. I think that might come in handy.

Although I know that doesn't preclude the existence of infinity. Seriously fuck these threads.

>>9571799
>larger than any given value
One number that is larger than any given value? No.
For any given value there exists a number larger than it? Yes.

>>9571804
After any NUMBER, there can only exist a larger NUMBER, provided there is no LARGEST NUMBER of which a NUMBER could not be larger.

Do you agree this is the claim?

>>9571392
I'm trying to prove that one doesn't exist only 0.99999999

>>9571811
I'll say if I agree when you write your claim in quantifiers about a well specified set of numbers so you don't pull the rug from under my feet and go "lellers I bet you didn't even realize that I use non-standard interpretations of these terms and now you agreed that infinity can't exist".

>>9571822
The only interpretation required is that of knowing english and being able to make logical connections.

>After any NUMBER, there can only exist a larger NUMBER, provided there is no LARGEST NUMBER of which a NUMBER could not be larger.
You agree this is the claim of infinity, and i'm sure you'll agree it is not an uncommon claim.

>After any number, there can always exist a larger number.
We can reliably know this to be true, if not true enough. If we said 99,999 was our example number, we can know in the very least that 100,000 is bigger and is too a number.

The only way to prove that a number exists where it cannot be incremented is to define a largest possible number. If everyone agreed 1 quintillion was the largest number, then once anyone reached 1 quintillion we would know to stop trying to add any more, so then we have a number that cannot have a larger number value relative to it. No one will recognize 1 quintillion + 1 has any real value, since 1 quintillion is already arbitrarily large enough to be useful for any real arithmetic. However, because we have a largest number the first part of the claim is no longer valid
>a larger real number exists after any real number
It's mostly accurate, but not perfectly accurate, so the claim must be altered.

But 1 quintillion isn't really the largest real number here in reality, so in our world the first part of the claim remains true and we agree that there is no largest real number, providing for the first part of the claim to always remain true.

>... provided there is no LARGEST NUMBER of which a NUMBER could not be larger.

The second part claims there can never be a largest number as such a number could not have a larger number after it, nullifying the first part of the claim.

Therefore infinity cannot be larger than any number as it would become the largest number, and if it truly weren't already treated as the largest number, infinity+1 wouldn't be seen as useless like like quintillion+1.

>>9571842
>You agree this is the claim of infinity
I don't agree to anything until you write the claim clearly in quantifiers about a specific set of numbers. Your game is the game of language tricks and intuition. Mathematics has replaced that by axioms and rigorous definitions because intuition doesn't work for these concepts.

>>9571842
As you can see, any prestablished definition FOR infinity cannot help but paradoxically state infinity does not exist, and i could prove this to you to a finite degree if you use any of the other various definitions prescribed to infinity, of which there are few and finitely many.

>sum of infinite series
I am too brainlet to grasp this

>>9571847
n=0;
while (x > 0){
n += 1;
Print(n);
}

This pseudocode is the equivalent of an infinitesum of +1 execution where every iteration partial sum is printed and readably knowable. Every print will always be a real number, and every print will always be larger than the previous print.
At no point will a print ever readout as [math]\infty[/math], therefore infinity doesn't exist as a number value.

If it doesn't exist as a number value, it cannot exist as a quantity. Infinity is then forced to exist by the sole definition of "never ending", even though the concept of never ending cannot be proven, but we could assume a base intent direction of it as "go and don't ever stop". With this being the only valid definition of infinity, to describe the pattern of 9's existing in 0.999... as "never ending, starting without stopping", then 0.999... can only ever equal itself and only itself at 0.999..., because anything more such as 1 would have brought some kind of end to what can only be endlessly unendable, where infinite sums cannot exist as objects but only as the values up to a real finite n'th limit because an unending, unendable limit of summation would never allow a result.

also dont be a faggot who cant read and thinks hes being tricked with words. You're only being tricked with numbers by choosing to believe infinity is rigorous or well defined. It isn't. Take it for granted that it isn't. At best it has one singular definition, that of unending work, yet few if any implements of infinity abide by this definition and instead treat it as an arbatrarirly large finite number where it's not infinite because it has no end, but instead because not enough information was provided to actually know what value it was. S h i t m a t h.

>>9571847
>>9571871
Put it this way, can you describe the exact difference between "an arbatrarily large real number" and "infinity", if infinity has a quantity value?

If i say to you "count from 0 to an arbatrarily large real number" and you agree to do so, do you think you'll respond with "which number?" If you did, i wouldn't tell you which number, i'd just repeat "an arbatraririly large real number".

This is the real trick that higher maths plays on you. In the realest sense of things, there is no different between infinity and the vague statement "an arbitrarily large real number", which means comparatively the quanitity of infinity IS an arbitrarily large real number.
You can't count to an arbitrarily large real number from 0 any more than you could count to infinity from 0. If infinity as a number and has a quanitity value, it is only as good as an arbatrarily large and undefined real number, and a vague undefined quanitity value is only as good as "???" Which means utilization of infinity would only be as realistically good as [math]\sum_{n=1}^{\rightarrow ???} \frac{1}{2^n}[/math] which is buttfucking retarded but literally exactly how it is used in calculus

>>9571770
>IF

>>9571930
X = 1;
IF (x=1){
>you're retarded
}
Yes, IF. What of it.

>>9571938
>infinety large
>real number

pick one

>>9571938
>>9571938
>infinitely large
>real number

pick one

>>9571949
I'm not saying infinity is a number, i'm saying it's "unending". Contrarily, infinity is used as a number in maths. You're not wrong, infinity isn't a number. I'm not wrong, infinity isn't a number. Maths is wrong though, because maths assumes infinity is a number, therefore mathematicians are wrong.

>>9571958
Infinity is a number, faggot. Just because it's not in [math]\mathbb{R}[/math] doesn't mean it's not a number.

>>9571958
>>9571963
[math]\overline{\mathbb{R}}, \widehat{\mathbb{R}}, \aleph_0, \omega, ...[/math], take your pick.

>>9571963
R is all real numbers. You're right, infinity isn't in R. Real numbers are all that matter. You need real numbers to do math. Math without real numbers isn't math.

>need real numbers to do math
>use infinity even though it isnt a real number
>pretend you're still doing math

>>9571958
>If an infinitely large arbitrary number can exist

It's your own fucking words.
retard liar

>>9571969
>Real numbers are all that matter. You need real numbers to do math. Math without real numbers isn't math.
t. never studied complex analysis
t. never studied DSP
t. never studied quantum mechanics
t. never studied QFT
t. complete brainlet

>>9571977
I was responding to a post talking about arbitrary numbers.

If infinity isn't a number, then an infinitely large arbitrary number doesn't exist. Any large arbitrary number could exist, but to be used as such they would have to actually be defined which number they are, as "arbitrary" is not useful in real number math. You can set up a situation where for any number, implicitly even arbitrarily large numbers, something can evaluate, but you must use a real number in these situations. You can't just leave the variable "an arbitrary number" remain undefined, it must be replaced with an actual real number to carry out arithmetic. "An arbitrary number" is used in place to describe any real number, even the numbers greater than any mentionable number. An arbatrarily large number can be any huge real number greater than any other mentioned number, but this only suffices as a variable awaiting replacement with a number. It has to be a number, it can't just remain undefined as "arbitrarily large".
There is a huge difference between getting the singular right answer in:
1 + x = 7
Versus getting the singular right answer in:
n + y = 8

There are innumerable ways to solve n+y=8, so how could you ever get the sole correct answers to the variables n and y? "There isn't enough information provided to properly solve it as intended." Is the only valid answer.

Using infinity in maths is the same exact thing as using an undefined, undefineable variable. You dont know the correct value of infinity no more than you know the actual sole correct value of n or y in n+y=8. You've left "infinity" undefined as "an arbitrarily large real number", forgetting to replace "an arbitrarily large real number" with an actual number value. If your limit is "an arbitrarily large real number", then you don't know when to stop. You don't know when that limit ends so you never stop, just identically the same as if the limit were infinity, ergo infinity = an arbitrarily large real number.

>>9571978
No field you just mentioned has real world value relative to physicality.
Enjoy learning fucking useless garbage where the only living you'll be able to make out of it is teaching it to college students who don't know any better but hope they're acquiring some useful information for their futures where probably none of them anticipate becoming teachers.

>>9572021
>No field you just mentioned has real world value relative to physicality.
confirmed brainlet

>>9572023
Ahuh, tell me, what has quantum field theory done for the world?
Quantum mechanics?
Surely something as early as complex analysis out to be useful.

Go on, i'm waiting.

>>9572010
>infinity = an arbitrarily large real number.

https://www.wolframalpha.com/input/?i=infinity
An unbounded quantity greater than every real number.

Infinity isn't a real number, by definition

protip: when you're in a hole, stop digging

>>9572024
https://youtu.be/gCAxGTt7nLg?t=8m

ITT.

A potential genius brings into question the meaning of numbers. Because he is a deep thinker.

Brainlets have no idea what he is talking about. Because they are brainlets.

>>9572024
I see you conveniently skipped DSP, cool. I know this is bait, but anyway:

https://en.wikipedia.org/wiki/Quantum_mechanics#Applications

>>9572028
By definition, it doesnt say what it is or isn't. It only says it is larger than any real number. This says nothing about infinity specifically, only its relation to something else. If it has no relation to real numbers, theres no point in mentioning real numbers. You are literally fucking retarded.

>>9572031
Yes, teaching it. Good job. Couldn't have fucked up that any better.

>>9572056
Maybe reread that link and actually learn how the things claimed to be derived from applications of quantum shit were actually invented before the field theories themselves.

Fuck the fuck off. You need quantum mechanics to make lasers and diodes work? No you fucking do not. Eat ass. You are literally a brainlet not because you tried to fill your brain with knowledge, but because you filled it with lies and retardations. Your brain is full just as much as would be required of someone who is intelligent, but it just happens to be full of nonsense instead of value.

>>9572059
>it is larger than any real number
if infinity were a real number
be definition it would be bigger than itself

lrn2read

>>9572061
>said the monkey of a book it couldn't read

>>9572071
>hand waving intensifies

>>9572059
>it is larger than any real number
if infinity were a real number,
by definition it would be bigger than itself

lrn2read

>>9572071
>Maybe reread that link and actually learn how the things claimed to be derived from applications of quantum shit were actually invented before the field theories themselves.
Sorry to break it to ya, but lasers and LEDs were invented after QM.
https://en.wikipedia.org/wiki/Quantum_mechanics#Electronics

>You need quantum mechanics to make lasers and diodes work? No you fucking do not.
Yes you do.

>Eat ass. You are literally a brainlet not because you tried to fill your brain with knowledge, but because you filled it with lies and retardations. Your brain is full just as much as would be required of someone who is intelligent, but it just happens to be full of nonsense instead of value.
k.

>>9572073
n = n+1

[math]\sum_{n=1}^{n+1}[/math]
Here's your "unending" operation. Heres how it should read. Easy. At n=1, the limit is 2. At n=2, the limit is 3. At n=3, the limit is 4. There you go. No infinity required, as a number or even a word to describe, and certainly not required as a symbol.

>Look at me i'm fucking isaac newton i'm a goddamned brainlet I GIVE THEE CALCULUS

>>9572092
>No infinity required
then it's finite

>yawn

>>9572099
Oh gee willickers, boys, we got ourselves one of them thinkers! An unending operation is finite! What an amazing analysis!
I guess since 0.999... has unending 9's in it, must mean there are a finite amount of 9's in it!
Don't even try asshole, 2/10.

>>9572109
>0.999...
has an infinite amount of 9's

not a finite amount
>infinity needed
>mind blown

>>9572092
as long as n is a real number that's finite
replace n with inf, now you've got an infinite result

infinity is required

>>9570309
It is when you look out.
Eternity lies within.

>>9572116
Infinite = unending
You assume "unending = finite"
Therefore infinite=finite, by your logic.
>>9572140
Unfortunately it's arbitrarily finite, meaning undefined and vague, so you cant increment from n=1 to n=infinity, unless you decide to change the sum's limit at some arbitrary point from n+1 to simply just n, stopping the unending work, but if its no longer unending, its no longer finite, and therefore no longer infinite.

Golly, its almost like it is literally impossible to use infinity properly. Fuck quantum mechanics, this is the true unknown for the ages. Every time someone tries to define infinity by a associating it with a number, it simply changes its own definition and can't be used!

>>9572155
>infinite=finite, by your logic.
nope

any n is a real number
infinity isn't

The only way you can get to infinity
is inserting infinity instead of n
Which just defeats the purpose.

>>9572091
The development of lasers needed masers to be developed. The development of masers relied on heating gasses. If increasing the temperature of a gas qualifies as quantum mechanics, then Hank Hill has a Ph.D in quantum mechanics. Unfortunately with such a shit field of useless knowledge, Hank Hill makes minimum wage selling barbecues instead of doing anything worthwhile for society.

The idea that masers would produce yielding results in analyzing hyperfine bullshit to 20 gigahertz is also bullshit. Atomic clocks aren't real. The tech to measure the oscillation value of ceasium-133 didn't even exist til the 90's, despite the atomic second coming about in the late 60's. At best it could have only been theoretically possible to predict using some made up form of uncheckable math what the hyperfine oscillation of caesium-133 could be, not realistically checkable and proveable. Worse yet that since the second were defined as however many gigahertz of radiation from caesium-133, this now invalidates the second because 1hertz = 1second. As if infinity being useless wasn't bad enough, the SI second is actually based on a value that required the second to have already been defined as something else. What fucking good is calling the second as "9 billion cycles per second"

Holy fuck. God exists but he did not make man. Nothing as dumb as man ought to be.

>>9572187
>Hank Hill has a Ph.D
>Atomic clocks aren't real
>God exists but he did not make man
KEK

>1hertz = 1second

>>9572187
>Hank Hill has a Ph.D
>Atomic clocks aren't real
>1hertz = 1second
>God exists but he did not make man
KEK

>>9572187
>The development of lasers needed masers to be developed. The development of masers relied on heating gasses. If increasing the temperature of a gas qualifies as quantum mechanics...
non-sequitur

>>9571871
>>9571905
Just because infinity isn't a real or natural number doesn't mean infinity can't exist. Infinity isn't a single concept but a collection of concepts. Saying a series equals infinity (in the extended reals) is saying the partial sums have no upper bound. You also clearly agree that the set of natural numbers exists and that it has no upper bound as for every natural number n there is a successor number n+1, what is the size of that set? That's another way the concept of infinity manifests itself.

>>9570343
Laser Light in which medium?
Light itself has no temperature, step up your unambiguity game.

>>9572462
Yes, you're right. infinity is a concept, not an implement, not a construct. If it were as simple as using concepts to define reality, all my conceptual game ideas would have already made me wealthy - i don't have to actually develop and market the games cause the concepts are just as good.

Protip, using a word attributed to vagueness to attempt describing something else as anything but vague is dumb.

>>9572512
The concept gives rise to different but related constructs that are well defined and don't lead to contradictions if you stick to the definitions. You refuse to do that and instead you handwave silly arguments based on intuition.

>>9571583
>Saying there are an infinite, non-finite amount of parts between finite 1 and finite 2 means you can never reach 2 from 1 by incrementing in those parts.
You can by doing infinite increments. This is just the same old Xeno's paradox fallacy. You're crossing infinite increments whenever you take a step, because each increment takes an infinitesimal amount of time to step over. But again, this doesn't even respond to the point since no one is computing the sum by adding each part incrementally. They are transforming that sum into something else. You didn't respond to anything I said, retard.

>>9571811
>After any real NUMBER, there can only exist a larger real NUMBER, provided there is no LARGEST real NUMBER of which a real NUMBER could not be larger.
FTFY

>>9570389
Temperature is always a measure of average translational kinetic energy so kindly fuck off. There is no such thing as negative kelvin as by definition 0 K equates to zero-point energy, the lowest possible energy a system can have under any circumstances.

>>9571871
>Every print will always be a real number, and every print will always be larger than the previous print.
>At no point will a print ever readout as ∞∞, therefore infinity doesn't exist as a number value.
Notice how you switched from "real number" to "number." Time to go learn elementary school math.

>>9571905
>Put it this way, can you describe the exact difference between "an arbatrarily large real number" and "infinity", if infinity has a quantity value?
What is a "quantity value"? Can you stop making up terms and just write a real argument. Because so far your argument doesn't exist. Oh and the difference is that the former is finite while the latter is not.

>>9572648
https://en.wikipedia.org/wiki/Negative_temperature

i like infinity

i didnt use to get it before

now i get some of it

its great

Do you guys want to know what I think?

>>9572764
No.

>>9572633
Xenos paradoxes include assumed finite elements. So no. Think again
>>9572655
>>9572646
>>9572666
Die in a tire fire you fucking retarded ESL loser.

>>9572910
>Xenos paradoxes include assumed finite elements.
Yeah a finite length divided into infinite increments you utter tard. You clearly have no response.

>>9573007
You're missing that the arrow paradox assumes an infinite quantity of freeze frames of an arrow in flight constitute the entire path of the arrow in flight, despite that no freeze frame is distinguishable from another because he assumes 0 time has passed between any frame.
Aka the retard would let that [math]0 × \stackrel{n}{\infty} > 0 [/math], n added to denote he's referencing the number infinity and not the "never ending, non-numerical increment" act of "infinitely" repetitive or increasing.
Since 0 × n = 0, he obviously had a misconception. Staring at a photo of an arrow in flight will never suddenly turn the photo into an animation showing where the arrow flies to, no matter how much time passes while having stared at the photo, nor does copying the photo innumerable times and arranging them in a flipbook allow the arrows flightpath to be animated.

The point is, you cannot make it to 2 from 1 in infinite increments unless you assume to abide by xeno's logic that 0×infinity > 0 [if not 0×infinity = 1], and if you assume this is the case then the utmost infinite'th partial sum of 1/2^n (achilles and tortoise) at n=infinity is [math]\frac{1}{\infty} = +0[/math], meaning the final required partial sum to sum totality is 0.
Extend this to 9/10^n, and at the infinite'th n, the infinite'th digit is 0, giving 0.999...0, where the "infinite repetition" is terminated by a 0 which prevents rounding up and also uniquely seperates the value with proper termination from 1.0 which could just as easily be written as 1.000...

To elaborate in solution, [math]\sum_{n=1}^{x} \frac{9}{10^n} = 0.9999[/math]
n=1: 0.9
n=2: 0.99 (+0.09)
n=3: 0.999 (+0.009)
n=4: 0.9999 (+0.0009); x=4, four nines
Provides evidence that the final partial sum must be a significant non-zero value to sum totality, but 1/∞ = 0 forces the final partial sum to be a value that cannot add anything extra to the sum in totality, providing for 1/2^n = 1 for any arbitrary n less than infinity.

>>9573192
>the infinite'th digit is 0, giving 0.999...0,

they're all 9's, cut the crap

>>9573192
C

1/2^n = 1 for any arbitrary n less than infinity is extracted from the provision that the reason 0 is being added at the infinite'th partial sum is because the sum has already reached its final summation and needs no more work, assuming 1/2^n=1 per the description of the paradox. If 0 is being added at the infinite'th partial sum, summation of significant values has been completed prior to the infinite'th partial sum, therefore it has summed not at n=infinity, but n<infinity, which makes n any arbitrary number, which extended to 9/10^n must mean, per the logics covered, that 0.9=1, 0.99=1, 0.999=1, 0.9999=1 etc.

>>9573192
>1/2^n = 1 for any arbitrary n less than infinity.

1/2=1
1/4=1
1/8=1
etc.

wow anon you solved it
the fields award is in the mail

>>9573222
Uhh.. that was zeno's solution, not mine.

>>9573210
In the very least it can be extended to instead show that 1/2^n=1 in a finite amount of increments, which is contradictory to zenos claim of infinite increments.

>>9573230
it's nobody's solution
learn how to write math correctly

>>9573279
Even if you were being intentionally retarded to disregard that I was talking about the sum 1/2^n which you should have known to read as [math]\sum_{n=1} \frac{1}{2^n}[/math], you would still have been wrong by calling it my work when i was showing it was zenos work.

Learn to read dude.

why does one grapefruit taste better than the other grapefruit? i bought 2 grapefruits but one tastes better.

>>9573333
>consuming mogrel racemixed citrus.

>>9573192
>Your concept of convergence leads to contradictions
>It's not me by being retarded and insisting that "0.999...0" is somehow a thing
>it's not me by ignoring the definition of convergence and instead claiming it can't converge in my unspecified intuitive model that I can keep changing in every post exactly because I never specified it
>it's not me by ignoring all the advances modern mathematics has made and instead falling back to 2000+ year old paradoxes
It's clear by now that you're either being intentionally retarded or you're just plain retarded.

>>9573380
Infinity has no value either as a defined idea or an applied concept. What the fuck advancements are you talking about. The whole point of this is that it is poorly defined loosely attributed vaguely described garbage good for no practical real world application, which is why it is not practically used in any real world application cause it doesn't have a constant intelligible definition, and to further accuse me of somehow falling back to zenos paradoxes when i was directly replying to zenos paradoxes being brought up as some shit idea intended to argue that infinity isn't loosely defined garbage is fucking full brainlet so good job, your sin is not my sin.

I change the definition of infinity to accomdate the explanation of any method which aims to support infinity, then i deconstruct infinity to non-existing within that methods own assumptions. You place a nail, i hammer it down, you place another nail, i hammer it down too. No definition of infinity is consistent or singular or useful. It is an invalid concept required for nothing.

>>9573210
>>9573252
Sum 1/2^n to any arbitrary n doesnt equal 1 though, so the assumption 1/2^n=1 is false. 1/2^n will only ever equal a value less than 1, because taking it to the infinite'th n will add a 0 partial sum meaning the total summable work ended prior to infinity, meaning it ended on any arbitrary n, and if we end on any arbitrary n, 1/2^n is evidently less than 1.

>>9570309
You need to understand the difference between addition and infinite summation. Then things not making sense will make sense to you. :)

>>9573513
Addition is real and infinity is not.

>>9573192
I don't know what a 0 length instant of time is, or how it's relevant, since convergent sums have terms that are finite nonzero. Try again, retard.

>>9573451
The assumption [math]\sum_{n=1}^{\infty} \frac{9}{10^n} = 1 [/math] is also false because the infinite'th partial sum is 0, meaning summable work completed prior to the infinite'th where n= any arbitrary number, where if n in [math]\sum_{n=1}^{\infty} \frac{9}{10^n}[/math] is any arbitrary number, obviously only equals an arbitrary but finite amount of repeating 9's.

>>9573519
Neither are real. Real mathematics is not 'real' either.

>>9573532
Convergence requires infinity to be rigorously defined in order to work because it is used on infinite sums. Unfortunately, there is no proof an infinite sum exists, much less proof infinity exists.

>>9573192
>The point is, you cannot make it to 2 from 1 in infinite increments unless you assume to abide by xeno's logic that 0×infinity > 0
Nope, one has nothing to do with the other. The arrow paradox fails because it doesn't coherently define any intervals of time. The other paradoxes fail because they are mathematically nonparadoxical.

>Since 0 × n = 0
n being a real number, not infinity. Multiplication by infinity is undefined.

> if you assume this is the case then the utmost infinite'th partial sum of 1/2^n
No such thing. All terms are nonzero, all terms correspond to a natural number, and there is no utmost. Once again you completely fail to understandwhat you're trying to argue against at the most basic level.

Saying that time is infinite does not mean that there is some time in the future that is infinitely far away from the present. Rather it means that all times in the future are a finite distance from the present, and there is no end time.

>>9573426
All you've shown is your own complete lack of understanding of the topic, not a lack of sense in the topic. Retard.

>>9573451
>because taking it to the infinite'th n
No such thing. Try again.

>>9573551
That doesn't respond to anything I said. Try again.

>Unfortunately, there is no proof an infinite sum exists, much less proof infinity exists.
Wrong. The two series discussed in this thread are proven to be convergent. And there is no proof that any number exists side they are axiomatic constructions.

>>9573561
I agree, infinity is "never ending", a direction, not a number.

Maths disagrees however.
http://www.wolframalpha.com/input/?i=Infinity
An unbounded quantity greater than every real number.

Quantity gives it numerical value, greater than every real number gives it a relationship with R and no other set.
This unending definition still doesn't allow for the Sums 1/2^n or 9/10^n to approach 1, however. If you dont end the summation, you don't get a defined result. This can instead be analytically extended to meam the only valid sum is to an arbitrary finite n, but doing this then clearly shows infinity was not required to obtain the sum at a finite n, and the partial sums to that n woild clearly define the sums finetely, squarely, and self-evidently less than 1.

If you wanna cut off some decimal places and be swell enough just rounding up to 1, feel free. Rounding is approximation though, not equality.

>>9573574
You are saying the end of sum 1/2^n doesnt look like [math]\sum_{n=\infty}^{\infty} \frac{1}{2^{\infty}}[/math], because an end can't exist, which means n/infinity doesnt occur, which means n/infinity doesn't need to be 0, which means that by never reaching the infinite'th n, there will always exist a not-insignificant non-zero value of [math]\frac{1}{2^{arbitrary real number}}[/math] required to add to the total of partial sums up to that point to equate 1.

i'm afraid you can't win, my good dude.

>>9573600
>I agree, infinity is "never ending", a direction, not a number.
Where did I say it wasn't a number? You seem to have a problem distinguishing between numbers and real numbers.

When time is represented as a real number line, of course infinity will not appear on the line and will only be an unattainable direction. But that doesn't mean it's not a number.

>If you dont end the summation, you don't get a defined result.
You do get a defined result in the case of convergent sums. Why do you think you don't get a defined result? Because you are viewing each step in summation as taking a certain amount of finite time. But again, this is incorrect since the actual method of evaluating a convergent sum does not involve infinite steps. You still have not responded to this fact.

>>9573633
>You are saying the end of sum 1/2^n doesnt look like ∑∞n=∞12∞∑n=∞∞12∞, because an end can't exist, which means n/infinity doesnt occur, which means n/infinity doesn't need to be 0, which means that by never reaching the infinite'th n, there will always exist a not-insignificant non-zero value of 12arbitraryrealnumber12arbitraryrealnumber required to add to the total of partial sums up to that point to equate 1.
Amazing, for the first time in this thread it seems you've written more than a few sentences of accurate mathematics. So where is the problem?

>>9573634
Oh no thats gross, dont be gay like that buddy. Infinity isn't a number. Math pretends it is, but as soon as you treat it like a number, it stops being intelligble. I dont care whether you think its a real number or a fake number or a complex number or a number outside of all sets. It doesn't matter at all what you think it is. The only thing that matters is what reality can do with it, which is nothing. Therefore it doesn't matter. Thats as basic as you need to go with it, no reason to try to argue about whether you believe i'm using the definition you're using at the moment of your next post which you will have arbitrarily flip flopped just like you'd done now from calling it never ending while chastising me for referencing zeno calling it a number, to then calling it a number yourself. Real gross behaviour buddy. You might be infinitely retarded.

>>9573639
Maybe you problem is just that you can't do math cause that post you seem to agree with explicitly states 0.999... doesnt equal 1, as there can only be an arbitrary real finite amount of 9's that could in the very least require 0.arbitrary finite amount 0's)1 to add in order to sum 1, even though you are arguing against this aren't you? That you think convergence is valid?

>>9573642
>The only thing that matters is what reality can do with it, which is nothing.
Without infinity you cannot construct the real numbers. Those are immensely useful.

Without infinity you have no advanced physics. That is immensely useful.

By your own argument, you lose.

>>9573652
You dont need infinity to do anything that has real world value. You are retarded if you believe otherwise.

>>9573650
>Maybe you problem is just that you can't do math cause that post you seem to agree with explicitly states 0.999... doesnt equal 1, as there can only be an arbitrary real finite amount of 9's that could in the very least require 0.arbitrary finite amount 0's)1 to add in order to sum 1, even though you are arguing against this aren't you?
You'll have to try again, this is just gibberish. As far as I can tell you're saying 0.999... has a finite amount of 9s, which is wrong. And no, it doesn't end in a certain number because it doesn't end at all. Plus you didn't answer my question. What is wrong with there being an infinite amount of nonzero terms?

>>9573654
>You dont need infinity to do anything that has real world value.
Math and physics have a lot of real world value. You lose.

>>9573664
THE MATHS THAT HAVE REAL WORLD VALUE DONT ACTUALLY USE INFINITY

>>9573654
Its not wrong. You agreed that sum 9/10^n will only ever have a finite number amount of 9's. You never reach the infinite'th step and can only ever have an arbitrary real n number step, so you always have an arbitrary real n number of digits.

Are you retarded?
You're retarded. I fuckin knew it dude i totally called it, you were gonna arbitrarily flip flop on your definition of infinity the next post and bam, thats literally exactly what you did.

Feel free to call me God or a time traveller or something.

>>9573678
THE MATHS THAT HAVE REAL WORLD VALUE ACTUALLY USE INFINITY

>>9573689
What is: None, Alex

>>9573678
>You agreed that sum 9/10^n will only ever have a finite number amount of 9's
Where did I do that? Lying and putting words in my mouth is not going to help you win the argument.

>You never reach the infinite'th step
No such thing.

>and can only ever have an arbitrary real n number step, so you always have an arbitrary real n number of digits.
There is no time factor here. 0.999... immediately has an infinite amount of 9s. You're spouting nonsense.

>>9573695
You dumb dumb.
You want infinity to be "unending".

So we use infinity as "unending" in [math]\sum_{n=1}^{unending} \frac{9}{10^n}[/math] okay? We're not worried about a quanity number of infinity even though thats how maths considers it, we're just gonna worry about the only logical way it ought to work as "unending" since the number version doesn't work.

So for the sum, we have 0.999... with an unending amount of 9's, right?

I'm gonna disregard your disallowance of time as a factor cause in due time you will try to say otherwise.

We have 0.999... with an unending amount of 9's. No end of 9's in sight. If you tried to count the 9's, you'd have counted an arbitrary amount because you cant count them all because they're unending.

So where exactly in this unending amount of 9's does it allow that it should equal 1? Lets be clear too, it's not just 1, it's 1.000... with an unending amount of 0's. If we created sets for each number 0.999... and 1.000... where each element in each set respectively were the individual digits, we would have unending sets with finitely numberable elements, where every identically accessed element of each set would be unequal
[0, 9, 9, 9, 9, 9, ...]
[1, 0, 0, 0, 0, 0, ...]
Totally unequal. Not a single element from either set matches up.

>>9573727
So what's the arithmetic mean of 0.(9) and 1?

>>9573727
>So where exactly in this unending amount of 9's does it allow that it should equal 1?
Where does "it" not allow it equalling 1? I don't see an argument anywhere, just a question of how convergence works, which you should already know if you passed high school.

>Totally unequal. Not a single element from either set matches up.
Luckily that is not a prerequisite for two decimal representations to be equal.

>>9573743
Now you're just using even more poorly described methodology by wanting yo assume convergence, even though its already established convergence requires a working definition of infinity of which, although "unending" is nice, is not how maths treats infinity. Maths says infinity is a quantity with a relationship to real numbers.

So again, you have to boldly face the fact that no element of 0.999... and 1.000... equate, nor any combination of elements up to attempting to include them all, and that any attempt to have a set featuring all the elements of either number will never be filled, but will have finitely many numerable elements in any attempt to do so, and assuming to hold all elements arbitrarily since we need not abide by non-arbitrary rules like time, will give us sets full of arbitrary real numbered elements with an arbitrary real length, which is really when you're starting to wish you put more of a wager on infinity as a quantity but none the less still proveable as a falsifiable attribute.

>>9573812
>Now you're just using even more poorly described methodology by wanting yo assume convergence, even though its already established convergence requires a working definition of infinity of which, although "unending" is nice, is not how maths treats infinity. Maths says infinity is a quantity with a relationship to real numbers.
It's both, depending on context.

And I have yet to see you even demonstrate you know the proof of convergence, let alone find a flaw in it.

>So again, you have to boldly face the fact that no element of 0.999... and 1.000... equate
So?

>>9571770
define this square as 1, no matter how you cut it, the parts are always summed to exactly 1.

>>9573840
You start with a square of arbitrary length sides. You cut this square in half. And color one half in. You have accomdated one half of the square, but one half is still left uncolored. You cut the other half in half and color in a half. You have accomodated one half and one quarter of the square, but one quarter is still left uncolored.

Every half cut you make of a half, leaves another half to be cut worth the same value as your previous cut. The only way to achieve a cut that leaves 0 left to be cut is to make a cur that leaves two equal halves of 0, one you can color and accomodate, the other you cannot, but its zero so it doesnt matter.

What number ÷ 2 = 0?

>>9573868
You can make unending cuts and fills of your newly acquired halves, but you will never have a total fillrate of 100%. There is no half you'll receive where a final cut will allow two halves of 0 value, so 1/2^n < 1

>>9574034
You can make unending cuts and fills of your newly acquired halves, but you will never have a total fillrate of 100%.
If you make unending cuts then you will have a total fill rate of 100%.

>There is no half you'll receive where a final cut will allow two halves of 0 value, so 1/2^n < 1
There is no final cut, so that's irrelevant.

>>9570325
What do you mean by this? Have you just said words to make it sound like you have something to say?

>>9574149
No cut allows for n÷2 = 0, you never get 100% fill. Whether or not a final cut exists is irrelevant.

>>9574242
>No cut allows for n÷2 = 0,
Which is irrelevant, since there is no final cut. You get 100% fill from the infinite, unending cuts, not any one cut.

>Whether or not a final cut exists is irrelevant.
Your argument is based on there being a certain cut at which there is 100% fill. Stop being retarded.

I was bored and wanted to know why [math]\sum_{n=1}^{\infty} \frac{1}{n}[/math] is considered divergent and seem to have accidentally discovered a constant which doesn't show up in google or recognized by wolfram as transcendent.
At n = 1,000,000 the sum is [math]14.392726722865 \vdots[/math], and
at n= 1,000,000,000 the sum is increased by this constant value of [math]6.9077552789821370 \vdots[/math], where at every [math]n= 10^{(x.mod3=0)}[/math], the sum increases by this value. Accurate to 29 decimal places using this value, i was able to predict at n=1 with 42 zeroes after it, the correct sum up to 4 decimal places by incrementing over n=1,000,000 as the base.

I'm also not sure but at 1 with 60 zeroes after it, the sum/(60+1) seems to be approaching [math]e [/math] albeit very slowly where at that point it is only 2.2743003,,,
Not sure at this point whether it would surpass e or not, but i assume the methodology would remain true for checking via [math]\frac{\sum_{n=1}^{10^{(x.mod 3=0)}} \frac{1}{n}}{x+1}[/math]

>>9574359
EVERY CUT OF THE INFINITE UNENDING CUTS NEVER RESULTS 0
YOU ALWAYS HAVE A SIGNIFICANT AMOUNT LEFT TO DIVIDE IN HALF YOU BRAINLET
ALWAYS
NEVER FILLS 100%

>>9574378
EVERY CUT TOGETHER RESULTS IN 0 BECAUSE THERE ARE INFINITE CUTS

INFINITE CUTS LEAVES YOU WITH ZERO LEFT TO DIVIDE YOU BRAINLET

ALWAYS FILLS 100%

>>9574359
>>9574378
Furthermore, because 1/infinity actually is 0 and infinity actually is treated as a quantity number, the only way to achieve a cut that results two halves of 0 value is to increment to the number infinity. 1/(2^infinity) = 0
Theres some problems here though since infinity isn't on the numberline, you can't actually increment to the number infinity, so you can't actually get that 0. You will instead only ever have access to 1/(2^n) where n is less than infinity, and what is less than infinity? Any arbitrary number is less than infinity. Which means all you will ever have access to in Sum 1/(2^n) is up to any definable real number n. Thats it.
Is Sum 1/2^n, n=1 to 10 = 1.0?
No?
then there exists no x for the Sum 1/2^n, n=1 to x which equals 1.0

>>9574378
LEARN WHAT A LIMIT IS
ALSO LEARN WHAT "CAPS LOCK" DOES

>>9574390
Jesus fuck you are retarded. You already know every cut up to infinity is not 0.
1/2^n at n=1 is 0.5 for fucks sake. Every cut thereafter is a non-zero value. You cannot arbitrarily redefine all previous cuts to suddenly equal 0.

>>9574390
>INFINITE CUTS LEAVES YOU WITH ZERO

so 1/inf = 0

>>9574399
0×infinity = 1 too, yes

>>9574394
>Furthermore, because 1/infinity actually is 0
Wrong, undefined.

>the only way to achieve a cut that results two halves of 0 value
This is not necessary to fill the square, it's irrelevant.

>Theres some problems here though since infinity isn't on the numberline
Which numberline?

>you can't actually increment to the number infinity, so you can't actually get that 0
There is no need to increment in the first place and no need to get an increment to 0. You have nothing but non sequiturs.

>>9574403
>undefined
http://m.wolframalpha.com/input/?i=1%2Finfinity

>>9574397
>You already know every cut up to infinity
This is gibberish, try again.

>1/2^n at n=1 is 0.5 for fucks sake. Every cut thereafter is a non-zero value. You cannot arbitrarily redefine all previous cuts to suddenly equal 0.
This has nothing to do with what I said, try again.

>>9574399
>so 1/inf = 0
So you are illiterate.

>>9574403
>>Furthermore, because 1/infinity actually is 0
>Wrong, undefined.
nah, it's zero
http://mathworld.wolfram.com/Infinity.html

>>9574407
>>9574408

>>9574405
It's undefined, Wolfram is wrong.

>>9574408
No, it's undefined.

>>9574413
>>9574418
KEK

>>9571638
>>9573192
>>9573210
>>9573451
>>9573540
>>9573633
>>9573678

> infinite'th

You keep using that word. I do not think it means what you think it means.

>>9574403
I have a square
I cut it in half and fill half of what i just cut
I now have 1/2 of a square filled and 1/2 of a square unaccounted for.
I cut the unfilled half in half and fill half of what i just cut
I now have 1/2 + 1/4 of a square filled, and 1/4 unaccounted for.
I cut the unfilled half in half and fill half of what i just cut.
I now have 1/2 + 1/4 + 1/8 of a square filled, and 1/8 of a square unaccounted for.

After every cut, you are that cut's value away from the full square
If you did this up to 1/2 + 1/4 + 1/8 + ... + 1/562,949,953,421,312 then there would still be 1/562,949,953,421,312 of the square left unaccounted for. Another cut will double this significand and HALVE the previous value to 1/1.12589991E+15, leaving 1/1.12589991E+15 of the square left unaccounted for. There needs to exist a value [math]\frac{\frac{1}{2^n}}{2} =
0 [/math] in order to no longer have any part of the square left unaccounted.
The problem of this square is the same as [math]\sum_{n=1}^{\infty} \frac{1}{2^n}[/math], which the sum shows an issue. If we assume Sum1/2^n is equal to 1 and leave the limit undefined and wish to know what the limit is, we can compare it to a problem [math]\sum_{n=1}^{x} \frac{9}{10^n} = 0.999 [/math]
n1: 0.9
n2: 0.99 (+0.09)
n3: 0.999 (+0.009)
Thus x=3 is our limit to solve this problem
Take note at x=3, the value added is not insignificant, which is why x=3
Back to [math]\sum_{n=1}^{x} \frac{1}{2^n} = 1[/math] where we wish to define x, if we set the limit to infinity, we have that the infinite'th partial sum is [math]\frac{1}{2^{\infty}} = \frac{1}{\infty} = 0[/math], which is an insignificant value. Whether this 0 is accounted for or not doesn't change the total sum, so this means that the end of significant summing did not occur at n=infinity, it occurred before at a value less than infinity. Since any real number is less than infinity, we are redirected that x= any R, but x= any R is obviously not 1.

Infinity is broken.

>>9574458
Infinity isn't broken, it just shows that it's impossible for the infinite sum of 1/2^n to equate 1.

>>9574458
>There needs to exist a value 12n2=012n2=0 in order to no longer have any part of the square left unaccounted.
False, if you gave infinite cuts then you have filled the square without this value. Try again.

>if we set the limit to infinity, we have that the infinite'th partial sum
No such thing. Try again.

>>9574467
The infinite sum of 1/2^n is equivalent to 1. All you've shown is a gross lack of understanding of basic math.

>>9574473
>>9574476
You are too retarded to breathe properly. Enjoy your hypoxia and brain death.

>>9574458
Think about what you are saying here: If there is a [math]\frac{1}{2^\infty}[/math], then [math]n = \infty[/math] which mean that there is an [math]x\in\mathbb{N}[/math] such that [math]n+x=\infty[/math], which obviously cannot ever be the case.
The notation [math]x \rightarrow \infty[/math], means that [math]x[/math] is approaching infinity, not that it will ever get "there" (a concept which in itself is nonsensical).

>>9574482
>t. lost the argument

>>9574486
Approaching infinity but never getting there is the same thing as saying all it will ever be is an arbitrary real number, and if the limit is any arbitrary real number then the summation halts at a value that is self-evidently finitely seperated from 1 by a significant value.

>>9570902
That's not what 'science' means.

>>9574493
>Approaching infinity but never getting there is the same thing as saying all it will ever be is an arbitrary real number, and if the limit is any arbitrary real number
You are confusing the limit with the variable approaching the limit. Laughable. Go to bed kid, you'll be late for school tomorrow.

>>9574493
To elaborate, the infinite limit doesnt imply that the sum value somehow reaches 1. It only allows that there will exist an infinitely long list of partial sums that get closer and closer to 1 but never produce a maximal partial sum that is evidently closest to 1 or exactly 1. The total sum at n=infinity is 1, but that's because we have exceeded the limit required as the partial sum at n=infinity is 0, which means their ought to have been an n before infinity where the partial sum was (an arbitrary value / 2) = 0.

The problem that is being exposed is that infinity as a quanitity has know implement of knowable difference from real numbers. There is a vague, undefined gap of values between any number and infinity, and the required value of significant/2=0 exists in this gap, where neither real number satisfies being the limit or does infinity satisfy being the limit. Using math, it is proveable that infinity is retarded because it has no direct knowable relation in difference from any other number, other than infinity-n = "some arbitrary number"

Infinity is broken.

>>9574491
were we arguing?
I was just holding my breath to make the fap more intense

>>9574519
>know
Typo, meant "no"

>>9574519
In short, it is mathematically proveable that when you write 0.999... or 1+2+3+4+..., that ellipses doesn't actually mean "to infinity", it instead literally means exactly what you're typing the ellipses to represent, that being "an undefined gap of necessary but missing information".

There you go. Infinity is not helpful. Its a lazy concatenation that gives you bad answers because invoking it deliberatelt invokes the idea that there is a significant amount of necessary information being omitted. Whether you use the number quanitity infinity or the never ending direction of infinity, as soon as you invoke it, you invoke that some information is unknown and unknowable, thereby sabotaging your arithmetic.

This might be my favorite thread on /sci/ ever. My mind is being blown.

>>9574533
BS, stop pulling crap out of your ass.
0.999... denotes the repeating decimal consisting of infinitely many 9's after the decimal point.

>>9574486
>n=∞
Implying inf is a real number. It isn't
http://www.wolframalpha.com/input/?i=Infinity
An unbounded quantity greater than every real number.

>>9574522
>being this insecure on an anonymous imageboard

>>9574542
Holy shit learn to read, that's not what I said at all.

0.999... means "0.999 and fuck math n shit i'm lazy"

Thats it. Thats defacto. Thats proven by using the implements of infinity prescribed by the very professors whose cocks you suck so much. This is not up for debate bro, it's fucking math, it's fucking fact.

>>9574552
>undefined gap

it's defined, retard

>>9574547
An unbounded quantity = a number
Only numbers can be quantities.

Greater than any real number = defines a relationship specifically with the real number set

Also 1/infinity in wolfram is 0.

>>9574555
If it were defined, infinity - n would equate a specific real number amount.
What is infinity-100?
Spoiler: the answer is you're retarded.

>>9574559
inf-100=inf

>>9574556
ts kiddo
>An unbounded quantity greater than every real number.
that's the definition

>>9574564
Infinity - n is a value less than infinity.
But it's not a real number value.
These are your numbers:
[math]\mathbb{U} = \big[ \mathbb{R} \big] < \big[ \infty - \mathbb{R} \big] < \infty[/math]

That infinity-R set in the middle is the undefined gap. Infinity minus any real number ends up there as some vague undefined undefinable bullshit because infinity is broken. Infinity - n can't be infinity, it has to be a value less than infinity, but the value isn't known unlike values inside R. Treating infinity as a set of arbitrary values to allow "infinity - 100 = infinity" then forces that no arithmetic performed on real numbers, even arbitrary undefined arithmetic, will allow the real number set to ever approach infinity. If the real number set never approaches infinity, the only result from an infinite sum could only ever be a real number limit result, and disregarding the real number limit then becomes a mathematical mistake which will allow errors to accumulate.

Stop

>>9574586
so what, that's the definition

>>9574586
>infinity-R set in the middle
doesn't exist, inf minus anything finite is still inf

>>9574559
It's still infinity but it's now a different infinity.

>>9574609
Couldn't care less. It exists and it doesnt exist. It exists, then inf-r is undefined shit, it doesnt exist then inf-r is still undefined shit. Either way the result isn't useful and forces the real number set to be seperated from infinity. Wolfram might say infinity - n = infinity, but it also says infinity - infinity is undefined, even though it makes all the provisions for n being allowable as infinity.

the gap exists whether its called infinity-r or left unaddressed, which is why (Sum1/2^n; n=1 to infinity) produces a 0 partial sum at an infinite'th n which denotes that a value of n prior to infinity is where the summable work actually completed since a partial sum of 0 makes no difference to the total sum. If you then try to work backward to determine where that n is, you either get an unknown value less than infinity in the infinity-r set, or you become unable to work backwards at all, like accidentally turning onto a one way street that somehow assfucks you and puts on the the freeway for 10 miles before you can turn around, except instead of 10 miles the freeway just goes off into space and you end up irreversibly flying outside of the galaxy. In other sciences, this is called "destructive", a situation where you cannot undo or work backwards from. If you increment to infinity in computer calculation (a defined number that exists as the singular largest value greater than the largest allowable double double, which ironically is an actual finite number that can be reached in increments), then the variable has essentially become destroyed. The value of the variable will exist at infinity but no amount of declination once you've reached that point will allow you to back out from infinity, and no increments will advance out of infinity. It is the death of the variable in terms of arithmetic until it is reset. Even this destructive behaviour isn't nominal however, and only exists because of poorly planned math implementations based on non-computer math

>>9574630
There are flaws in your reasoning
You think infinity is a number
You think that there is only THE infinity.

>>9570309
Anyone who tries to argue against the concept of infinity using only intuition and metaphorical explanations with very basic usage of actual maths are like those annoying weebs that think they know Japanese and fervently argue about the correct translation but still have to rely on subtitles for watching their anime.

>>9574631
No, i think infinity is anything anyone wants to make of it, but every way anyone ever uses it defies arithmetic and preclude allowing infinity to be useful.
I clearly stated two different accomdations for infinity there. A maximal value where -r puts it in a different set, or a fucked set of values where -r gives it a different infinite identity part of the infinite set.

>>9574630
>(Sum1/2^n; n=1 to infinity) produces a 0 partial sum at an infinite'th n
Where did you get this idea from?

>>9574642
1/infinity = 0
[math]\sum_{n=1}^{\infty} 1 = \infty[/math]
Where'd you get the idea to question it?

>>9574643
That would equal to 1, not infinity. There is no n to evaluate. Perhaps you meant
[math]\sum_{n=1}^{∞} n= ∞[/math]?

>>9574646
No. I described 1+1+1+1+1+1+ and so on. You described 1+2+3+4+5+6+ and so on. n doesnt need to be a variable in the summation itself, n only defines how many iterations of the summation occur. This is why 1/2^n is
0.5 at n:1
0.75 at n:2 (previous 0.5 from 1/2 + current 0.25 from (1/[2^2]) aka 1/4

Etc.

>>9574650
>1+1+1+1+1+1
that would be [math]\sum_{n=1}^{∞} 1^n = ∞[\math]
>doesnt need to be a variable in the summation itself, n only defines how many iterations of the summation occur
You can't even get your notations right. The equation that the sigma notation is evaluating needs to be a function of the number of iterations.
[eqn]\sum_{n=a}^{b} f(n)[/eqn]
The rest is just garbage spewed from misconceptions.

>>9574658
>math]\sum_{n=1}^{∞} 1^n = ∞[\math]
meant to be
math]\sum_{n=1}^{∞} 1^n = ∞[/math]

>>9574659
[math]\sum_{n=1}^{∞} 1^n = ∞[\math]

>>9574658
http://m.wolframalpha.com/input/?i=sum%5B1%2C+%7Bn%2C1%2C6%7D%5D+and+sum%5Bn%2C+%7Bn%2C1%2C6%7D%5D
I thought you were legit asking how to do use sums but i guess you're just an idiot.

>>9574630
>Couldn't care less
fine, ignore math

it's m-muh f-feelings from that sentence on

>>9574630
aand a word salad wall of text.
classic rambling lunatic style.

>>9574669
>hand waving

>>9574672
>thinks that computers prove the limits of math and not the other way around

>>9574672
>counterargument is literally a pic of hand waving

>>9574679
>get called out for handwaving and being a brainlet who can neither read or do math
>young black woman says stop.jpg
>continue handwaving anyway while still being unable to read or do math
>expect to be taken seriously
>don't get taken seriously
You are a walking existential crisis, boy.

>>9574682
>no math, just m-m-m-muh

this fucking thread yet again

>>9573812
How can the sequences [math]\left(\frac 1 n \right)_{n\in\mathbb N_0}[/math] and [math]\left(\frac {1}{2n} \right)_{n\in\mathbb N_0}[/math] have the same limit when none of their elements are equal? Infinity is clearly retarded.

>>9574785
1/4 isn't 1/(2*2)

[retards applauding intensifies]

>>9574785
There is no *one* infinity. There's a reason why ∞ - ∞ is undefined instead of zero.

>>9574519
>To elaborate, the infinite limit doesnt imply that the sum value somehow reaches 1.
Yes it does.

>It only allows that there will exist an infinitely long list of partial sums that get closer and closer to 1 but never produce a maximal partial sum that is evidently closest to 1 or exactly 1.
It also means that the series itself, not partial sums, are equal to 1.

>The total sum at n=infinity is 1
OK so you admit you were wrong this whole time. Thanks for playing.

>but that's because we have exceeded the limit required as the partial sum at n=infinity is 0
There is no partial sum at n=infinity

>>9574559
>If it were defined, infinity - n would equate a specific real number amount.
Wrong.

>>9574637
>No, i think infinity is anything anyone wants to make of it,
Which is obviously wrong since you keep using it in nonsensical ways that defy real mathematics.

>but every way anyone ever uses it defies arithmetic and preclude allowing infinity to be useful.
Because to a complete novice like you arithmetic is the be all and end all of math. Pathetic.

infinity is a concept, not a number

>>9574643
How does that justify an "infinite'th partial sum"? Answer the question.

>>9575085
It must. If you don't assume to arbitrarily reach the infinite'th partial sum, that means you're assuming no zero, that means you're assuming the sum will never reach an end, that means you're assuming that all possible values are real number values, that means you're assuming there must exist a smallest real number part such that adding it to 0.9 repeating (which is repeating to a real number value because you assume infinity can't be reached) will result 1.

This is no joke. Whether you pretend to understand infinity or not, there is little but absolute truth behind the fact that it's vagueness in usage can be analytically extended to forcing it to produce results it cannot accomodate for itself, such as this result that an infinite'th partial sum is 0 value and summable work finished prior to infinity. The only thing anyone ever have needed to know is that infinity is greater than all real numbers, so less than infinity then defines any real number. If you replace the direction from infinite'th n which was too much to any real n, you then get a properly finite result. There is no real solution x to the problem [math]\sum_{n=1}^{x} \frac{1}{2^n} = 1 [/math]. Infinity is too much, any real number in x is too little, and this partially extends from the fact 1/infinity = 0. This doesn't mean 1/infinity isn't 0, cause if we assume it isn't then we still have the same problem above that infinity is never approached in the first place, or that 1/inf would be an undefined non-number where upon reaching the infinite'th n would returj some kind of problem.

Anyway the pont is 1/inf = 0, 0/2 = 0, you now have a half cut that leaves nothing uncut and have accounted for all 100% of the square. If you presume to never reach infinity, you never get to make the final cut. If you presume to reach infinity you make a cut on zero, not to zero, meaning you ought to have finished cutting before infinity in some real numbered step, yet no real numbered step exists to solve.

>>9575355
Maths not getting accuracy right is the difference between a quantum teleportation device sending all your bits from point a to point b, or that same quantum device discarding random atoms of you during every teleport or accidentally merging you with errant particles of dust. Too much or too little is unaccepetable.

>>9575077
I've used it as a number as defined by mathematics. I've used it as a direction, as defined by reasonable feeling of how it should be. I've used it as a singular value. I've used it as a set of values.
Using infinity in any variety of ways doesn't allow it to work. No way works.
Infinity doesn't work no matter how you use it.

>>9575482
1/inf = 0 works just fine

>>9575482
Theorem 1: For all definitions of infinity, it holds that the definition is inconsistent.

Proof:
We prove this by example. Define [math]\infty[/math] as the largest natural number. It then follows that [math]\infty + 1 = \infty[/math]. Since it's true that a natural number subtracted by itself yields 0, it clearly follows that [math](\infty + 1) - \infty = \infty - \infty = 0[/math]. However because addition is commutative it also follows that [math]\infty + 1 - \infty = (\infty - \infty) + 1 = 0 + 1 = 1[/math]. This proves that [math]0 = 1[/math] and as such we've shows that this definition of infinity is inconsistent.

Because we provided a counterexample, it follows that all definitions of infinity must be inconsistent. This proves the theorem. QED.


Checkmate infinitists.

>>9575534
wrong

>>9575534
nice

>>9575534
>∞−∞=0
That's where you're wrong. Subtraction of an infinite quantity from itself is undefined. It doesn't make ∞ inconsistent anymore than the fact that 1/x is undefined at x=0 makes division "inconsistent".

Infinitists and finitists are both right.

Numbers are infinite, but our limited brain capacity means we perceive and use them as finite things, just as we perceive our 10 fingers/thumbs as finite things, with a beginning and an end. But there is no official beginning and end to one's fingers, just a rough approximation that is useful enough to make the distinction, and it's the same with numbers,

>>9575534

itt: people trying to understand infinity despite
our brains are incapable of it

>>9575520
1/infinity=0 treats infinity as a number. I've already shown what treating as a number entails. It allows that an infinite sum n=1 to infinity could, even arbitrarily, acquire a partial sum at n=infinity, but such a partial sum is 0. This means two bad things.
1) as the partial sum is zero, the partial sum is irrelevant to the total sum, meaning it wasn't required to reach n=infinity to finish all summable work, ao you must work backwards to a value less than infinity. Since that the only values less than infinity are all real numbers, any real number value substitution for n is used, but doing this provides no reasonable solution as no real number divided by another real number is 0, so you simply can never have a finitely singulat correct solution to an infinite sum. Any real number n validates as a solution up to any real number of decimal places, but the solution limit for any [math]\sum \frac{x}{(x+1)^n}[/math] such as 1/2^n or 9/10^n can then only equal a finite number that is finitely seperable from 1. 0.999... =/= 1

2)if infinity is a set of values, having an infinite amount of 0 partial sums would then equate to 1, as 1/inf=0 so 0×inf=1, so we now have 1+all prior partial sums which means the total sum approaches [math]1.\bar{9}[/math], not 1. n=infinity is yet again proven to be too much and all required summable work must have occurred before infinity, but any real number n in the sum shows that x/(x+1)^n cannot finitely equate 1.

>>9575534
>>9575586

>>9575571
Buddy it's true if [math]\infty[/math] is defined as just another natural number. I was showing that the definition where you treat it as a natural number is inconsistent. It then logically follows that every other definition must also be invalid, as mentioned by >>9575482

The logic is flawless, just accept that infinitists are done.

>>9575598
>Buddy it's true if ∞ is defined as just another natural number.
this doesn't mean anything

>>9575571
If you think that's where the proof goes wrong you should probably never touch math again.

>>9575598
>The definition where you treat it as a natural number is inconsistent. It then logically follows that every other definition must also be invalid
non-sequitur

>>9575628
https://en.wikipedia.org/wiki/Extended_real_number_line#Arithmetic_operations
That's literally where it goes wrong, faggot. ∞−∞=0 is flat-out wrong because it leads to a contradiction.

>>9575534
>Define ∞ as the largest natural number
how about not
https://www.wolframalpha.com/input/?i=infinity
An unbounded quantity greater than every real number.

try again

>>9575658
Learn to read english you ESL shitter >>9574556

>>9575665
ditto

>>9575658
Just read the proof again, and read the theorem too. If you weren't a complete shitter you could find the actual error in that proof. Protip: if you're a retarded engineer that has never written a proof, don't even try, you're not up to it.

>>9570487
What if I allow Axiom of Infinity but limit Axiom of Powerset to finite sets?

>>9575665
no one gives a rat's ass about your
made-up math in >>9574556

stick to the actual definition at >>9575658

>>9575534
>We prove this by example.

lol

>>9575592
My favorite part about this is the implication that you could finish counting all possible finite numbers and still be unable to reach infinity even after every possible number had been accounted for. It just goes to show that a definition of "greater than all other numbers" is positively meaningless, especially since everyone already knows a greatest number can't exist, where these two statements obviously contradict each other. Infinity as the greatest number yet no greatest number exists only lets infinity then not exist.

>>9575592
>1/infinity=0 treats infinity as a number
nope, if inf were a real number, the ratio wouldn't get down to zero

An unbounded quantity greater than every real number.

>>9575694
You don't even fucking know what a number is and I have berated you multiple times in this thread already over all the other dumb shit you've said. Fuck off dude. You're not welcome.

>>9575688
>infinity then not exist

or infinity is not a real number
because that's what >>9575658 says

>>9572086

>>9575707
The way I see it numbers are just whatever object you want to call numbers. They don't have to share any property with any other kind of number other than being called number.

Is that wrong? If so, what are the defining properties of numbers?

>>9575707
Fuck off dude. You're an asshole

>>9575718
You want to call dozen a quantity, you gotta accept that the quantity is a number and that number is 12.
Infinity as a quantity requires a number too, but instead of a number all you get is "???". Cant really do reasonable addition and subtraction on what can only best be described as an undefined variable.

Its the difference between solving 1 + X = 7 versus Z + 1 = W
X oughta be 6, but you can't know what Z or W are supposed to be. Infinity as a number is the equivalent of an undefineable variable, because it has a quantity but no provided number value to associate with that quantity, unlike the quantity dozen being associated with 12 or the quantity couple associated with 2.

>>9575762
>You want to call dozen a quantity
I don't want to do anything other than ask what the defining properties of "A number" are.

>>9575784
A number is an exact quantity, defineable by the decimal system and the characters 0123456789

>>9575707
lol you sound like a real fuckin loser

>>9575808
That makes complex numbers not numbers, which is stupid. What you're saying makes being a number equivalent to being a real number, but we already have a word for that, it's 'real number' so that's stupid.

>>9575808
you agree to find me two exact same grapefruits, and ill agree to your idea of numbers

>>9575820
I completely deconstructed infinity and you're calling me a loser, even though the only reason you'd be such a bitch to call me a loser is cause you yourself lost and are spiteful.

Don't project your own insecurities onto others.

>>9575834
Grapefruits aren't numbers...

>>9575841
hold up fella we got einsteinowitz ova heaa

>>9575837
>I completely misconstrued infinity...

FTFY

>>9575848
I told you to stop projecting. If you don't know how to do that, then stop posting.

>>9575860
fuck off asshole
you're an asshole and don't know shit
how's that for a paradox

Heres a good way to illustrate the point. Do you need infinite money?
Even if you were the most greedy person ever, do you need infinite money? Cause i'm pretty sure you'd be able to accomplish anything you want with just 1 trillion dollars. You could probably do well enough with 1 billion or even 1 million. You need need infinite money and you could accomplish everything you want with just a finite amount of money.

You can accomplish everything you need to with just finite numbers. No one needs infinity to exist. You don't even need an infinite amount of real numbers.

You don't need infinity. Its simply too much for you.

>>9575482
>I've used it as a number as defined by mathematics.
No you haven't, you've done the opposite.

>>9575355
>If you don't assume to arbitrarily reach the infinite'th partial sum, that means you're assuming no zero
Wrong.

>>9575534
>Define ∞∞ as the largest natural number.
Wrong.

>>9576139
I'm a retard and I approve this message

>>9576139
>Even if you were the most greedy person ever, do you need infinite money?
Non sequitur.

>You can accomplish everything you need to with just finite numbers.
No you can't. You can't construct the real numbers, you can't do most of modern math and you can't do most of modern physics. You are in denial.

>>9576167
Demonstrate infinity as a number. Provide an example. It doesn't suffice to simply call me wrong. The burden of proof is on you to prove I am wrong, so try to prove I'm wrong.

>>9576219
All real numbers are finite numbers.

Heres more to work out how needlessly big infinity is.

The infinite sum 1/n is a number that grows incredibly slowly. At n= 1,000,(467 more zeroes), the sum is only something like 2,000.
If we took the sum from 2,000 to 100,000,000, the limit at the new sum would be a 1 with 16 million zeroes after it. If we took the the sum from 100,000,000 to 100,000,000,000,000 the limit at the new sum would be a 1 with 16 trillion zeroes after it. If you took the sum to 100 googols, the limit would be 1 with 16 googolplex zeroes after it.

1000 thousand
1000000 million
1000000000 billion
1000000000000 trillion
1000000000000000 quadrillion
1000000000000000000 quintillion
1000000000000000000000 sextillion
1000000000000000000000000 septillion
1000000000000000000000000000 octillion
At octillion this number is retardedly large at 1 with 27 zeros after it, yet even this number is miniscule compared to the first mentioned number at 1 with 470 zeros, and all of these example numbers are definitely finite yet still less than arbitrarily large which is further still smaller than infinity.

The smallest unit of length is [math]\frac{1}{10^{44}}[/math] or a decimal followed by 44 zeros


The smallest number based on the number i started with at the top of the problem is [math]\frac{1}{10^{470}}[/math]. The planck length compared to this number is equivalent to taking a planck length, stretching it across half the distance of the entire universe, then taking a planck length measurement within that region

>>9576273
>Demonstrate infinity as a number.
What does that mean?

>The burden of proof is on you to prove I am wrong, so try to prove I'm wrong.
No the burden of proof is on you to make a coherent argument.

>All real numbers are finite numbers.
So? Do you know the construction of the real numbers? Do you even know what that means? You are laughably ignorant.

>>9576381
>The smallest unit of length is 1104411044 or a decimal followed by 44 zeros
That's not a unit of length.

> The planck length compared to this number is equivalent to taking a planck length, stretching it across half the distance of the entire universe, then taking a planck length measurement within that region
You can't compare a planck length to a dimensionless number. That makes no sense.

>>9576416
retard

>>9576403
>you're wrong but i can't prove it

>>9576435
>infinity is wrong but I can't prove it

>>9576381
so?
are you trying to impress a six year old?

>>9575808
>A number is an exact quantity, defineable by the decimal system

>>9576273
>Demonstrate infinity as a number.
Ok. According to the usual construction of real numbers from the rationals by Dedekind cuts, a real number is simply the set of rational numbers that are strictly less than it. Hence the empty set [math]\varnothing[/math] represents [math]-\infty[/math] while the set of all rationals [math]\mathbb{Q}[/math] represents [math]\infty[/math].

>>9576175
No. It's correct in the context of that proof. You could argue the wording is awkward, but then you're just being pedantic.

>>9576965
>It's correct
nope
https://www.wolframalpha.com/input/?i=infinity
An unbounded quantity greater than every real number.

>>9576965
>ignores the context of the proof
You're intentionally being retarded, right?

>>9577006
Context is absolutely key.

>>9576832
How is arithmetic defined in the dedekind cuts construction? Don't you need non-empty sets on both halves of the cut for this to be consistent? (Assuming we want to retain the properties of a field)

>>9570309
Your pic is wrong btw

>>9570389
>negative kelvin
Kill yourself
I'm a maths major but I remember physics from high school. Absolute zero hasn't even been reached brainlet

>>9577149
You can define temperature as some relation between the energy and entropy of a system which lets you imagine systems with negative temperature, but it's not the standard definition.

>>9577141
Indeed, everyone knows ellipsis should have 3 dots, not 5.

>>9576820

Sometimes feels like i'm talking to 6 year olds when you refuse to let go of infinity. You can't prove to have used infinity up to a value with 16 trillion decimal places.

>>9575825
Complex numbers arent numbers, they're just a poor mistake by brainlets who dont understand axis exist.

When they finally flesh out all the describable properties of a number and its interactive/relative properties to other numbers, there will be a way to represent that as the human form.


1In the beginning was the Word, and the Word was with God, and the Word was God. 2He was with God in the beginning.

>>9574458
Could infinity simply be any value greater than any local required limit?
Dead simply, 1+ x = 3
x can only be "2" if the rule of the variable x is that it isn't a compound equation like "(1+1)" or "(3-1)" or "[math]\frac{6}{3} [/math]"

Infinity in relation to x would be a value that is too much, a value greater than 2, as 1+3 = 4, 1+4 = 5, etc. We assume to do work until a solution is found regardless of direction to do it in a certain number of steps, so we need not define the work to be done on arbitrary arithmetic with a limit. However, on math with limits, setting the limit to infinity becomes properly needless as the limit is then greater than required, since infinity as value greater than the local limit is evidently greater than required in 1 + x = 3. "Greater than required" is also sufficient in decribing the partial sum problem at n = infinity when substituting n in the sum with infinity. "Greater than required" is also read as "too much".
1 divided by a value that is "too much" then equals 0, because too much in relation to real numbers is a value that is outside all real numbers. So with a local finite limit like 2, infinity would exist inside the real numbers at any value > 2, but without a local finite limit such as the limit is infinity itself, infinity would exist outside the real numbers so infinity cannot be a limit at all, and can only be defined as greater than the local finite limit of which all arithmetic must have local finite limits.

[math]1 + \stackrel{x}{1} < 3 \\ 1 + \stackrel{x}{2} = 3 \\ 1 + \stackrel{x}{\infty} > 3[/math]

>>9570309

>>9577959
>so bad it's not even wrong

>>9576832
Tbh senpai the idea of dedekind cut doesnt really make sense by itself so extending beyond it isn't valuable.

>set A contains every rational number less than the cut, set B contains every rational number greater than or equal to the cut
Provides that B is greater than A, that if B were infinite then A would be finite, provides that A to B, 1 to any n, can only have a finite amount of elements in it's set.
Meaning 1 approaching 2(non-inclusive of 2) can only have a finite amount of values between 1 and 2, and 2 going on would have infinite, which already assumes a definition of infinity is in place. The set A from 0 towards any arbitrary real number Z would only be abled to have a finite number of elements, and the set B from Z onwards would only have a greater number of elements as it includes Z where A does not.

>>9577997
>Provides that B is greater than A
If you are tapping about cardinality, that's wrong.

> that if B were infinite then A would be finite
Wrong.

>provides that A to B, 1 to any n, can only have a finite amount of elements in it's set.
Wrong.

>Uniformed: the post: the board

>>9578051
>A set partition of the rational numbers into two nonempty subsets S_1 and S_2 such that all members of S_1 are less than those of S_2 and such that S_1 has no greatest member
Explain

>>9578085
You are confusing the size of the members with the size of the set, cardinality. The cardinality of the sets are equal. They are both countably infinite.

>>9578107
This isn't helpful then. Of course the values between 0 and 1 would be smaller than the values between 1 and 2. This doesn't help to define infinity.

>>9578158
What defines infinity as a number is the dedekind cut between the empty set and the set of all rationals. You asked for a demonstration of infinity as a number. You were given it. I don't know what more you want.

>>9578158
How are the real numbers constructed then?

>>9578169
Dedekind cuts requires no set can be empty.

>>9578238
That's only a requirement for constructing the real numbers. Infinity isn't a real number.

>>9577959
1+x=3
X could be the sum of any positive divergent summation and any negative divergent summation.
Basically any (+inf) + (-inf) summation can equal any real number.
t. Reimann's paradox

>>9578258
But you said that the amount of values in the sets wasn't what mattered, just the values themselves. All real numbers in the set that isn't the empty set doesn't mean it is infinite, just that all the values in the set are greater than nothing.

This doesn't help to define infinity.

>>9578266
>Basically any (+inf) + (-inf) summation can equal any real number.
Wrong. You can't rearrange 1+1+1+... To converge to anything.

>>9577997
>Meaning 1 approaching 2(non-inclusive of 2) can only have a finite amount of values between 1 and 2
Then exactly how many real values are between one and two?

>>9578281
Positively divergent and negatively divergent
Read the whole post next time.
Also assume it is a continuous summation and not discrete

>>9578274
>All real numbers in the set that isn't the empty set doesn't mean it is infinite, just that all the values in the set are greater than nothing.
You have it backwards. Positive infinity is constructed by having the set of all rationals be the set which positive infinity is greater than.

>>9578266
If a value in x doesn't solve 1+x=3, but is less than 2, it is a value that is too little. If a value in x doesn't solve 1+x=3, but is greater than 2, it is (locally) infinity. This isn't attempting to define infinity as a number, but rather a property of "excessiveness beyond correct for solving the problem"
As such, there exists no infinite summation, as this definition of infinite would be summation above and beyond acquiring a reasonable answer.

>>9578291
Yeah, thats not a different definition than "a number greater than all numbers", which has already been buried as a fallacy.

>>9578298
Where did you bury it as a fallacy?

And if you don't accept that then you can't accept the construction of the reals.

>>9578303
You dont need to limit numbers to existing or not based on dedekind cut. Its not useful by itself.
Furthermore the original question wasn't "how do you construct infinity", it was "use infinity as a number in a way that disproved my claims of infinity used as a number having clear and evident issues".

>>9578293
The addition of an infinitely positive and an infinitely negative summation can equal any real number arbitrarily. Read about riemann's paradox.
By ordering the terms in the infinite summations differently you can group them in such a way as to have it equal any real number you would like
This only works when adding an infinitely positive Divergent series and an infinitely negative Divergent series

>>9578314
>You dont need to limit numbers to existing or not based on dedekind cut.
Where did I do that?

>Furthermore the original question wasn't "how do you construct infinity", it was "use infinity as a number in a way that disproved my claims of infinity used as a number having clear and evident issues".
Wrong, it was "demonstrate infinity as a number."

Not to mention that you have not shown any issues with infinity so there is nothing to disprove. All of your alleged issues have been shown to be based on simple fallacies in your reasoning. Look at any of your posts in this thread and find me one that has not been addressed.

>>9578324
Infinite summation has no meaning. It requires infinity to be rigorously defined. You're a step ahead of the topic.
Infinite summation when infinity is treated as a number, and therefore a limit, insures that no infinite summation properly sums what had classically been claimed as the result. This is demonstated here >>9575592
[math]\sum_{n=1}^{x} \frac{1}{2^n}[/math] cant equate 1 for any x limit, including infinity. When the limit of infinity is used as a number, it can be used to mean the summatiion never ends therefore any test of n will always be a real finite number, or it means n=infinity can arbitrarily be achieved, but [math]\frac{1}{2^{\infty}} = \frac{1}{\infty} = 0[/math] means at n=infinity, 0 is being added which means all summable work occurred before infinity at an n less than infinity, yet any n less than infinity used as the limit doesn't allow the result of the sum to reach 1 nor is the sum "infinite" any more, and this was if infinity were a singular value. If infinity were a set of values itself infinitely long, at n=infinity there would be an infinite amount of partial sums of 0, which 1/inf = 0, 0×inf = 1, which means all partial sums added are 1 + (1/2^n for all real n) which is a sum not approaching 1, but instead a sum approaching 2; in the very least.

>>9578353
>∑xn=112n∑n=1x12n cant equate 1 for any x limit, including infinity.
x is not a limit, and it equates to 1 when n = infinity

> yet any n less than infinity used as the limit doesn't allow the result of the sum to reach 1
So what? Different values of n give different values.

>nor is the sum "infinite" any more
It's still infinite.

>which 1/inf = 0, 0×inf = 1
No, it's undefined.

All of your issues stem from assuming that infinity must have the same properties as a finite number, when by definition it doesn't. So the failure is solely yours.

>>9578367
1 divided by infinity is zero. You are not arguing with me by claiming otherwise, you are arguing with math.

You are just shit at reading and a stupid dickhead so whatever. You are actually wrong. You're wrong about this and you were wrong in your last post when claiming the original question wasn't to use infinity as a number.
>>9576167
I used it as a number, the argument was i hadn't.
>>9576273
I then said demonstate it as a number, to appease how I hadn't already used it as a number

>>9578367
>limit is x
>"x is not the limit"
x is the limit, dude.

>>9578382
>1 divided by infinity is zero
In some contexts like complex analysis it is. But it's generally undefined. This is irrelevant anyway as the big mistake was assuming that this implies that infinity x 0 = 1. This assumes that multiplication by infinity is defined.

And you didn't reply to the rest of my post, I guess that means you concede the other points and admit your argument fails.

>you were wrong in your last post when claiming the original question wasn't to use infinity as a number.
You said it right here >>9576273 "Demonstrate infinity as a number." The stuff you put in quotes as if you said it appears nowhere.

>I used it as a number, the argument was i hadn't.
No the argument was that you hadn't used it as a number as defined by mathematics. Learn how to read.

>>9578393
>>limit is x
No it's not. Do you know what a limit is?

>>9578476
If 1/inf = 0
0×inf = 1
Do you not know how to do math? Division and multiplication aren't some abstract things, they're just glorified addition and subtraction. 1/inf = 0 means if you have infinite 0s, adding them together equates 1, ergo 0×inf = 1. More realistically, n/inf = 0, so 0×inf = n, which is just one more invalidating issue of many regarding what happens when using infinity.
I did reply to your post in general by calling it wrong, because it was. You took assumptions, defacto granted shit, and argued against them. This makes you wrong. This makes you as wrong as if I called the sky blue and you said it wasn't, that it were instead green. No one needs to prove the sky is green and you're objectively wrong for arguing, and if you're that wrong its easy enough to just disregard you as nuts. You continue being wrong and arguing about what I posted myself, asking infinity be demonstrated as a number, which you misconstrued to "construct the number infinity with dedekind cut" which 1, didnt use infinity as a number, and 2, was an arbitrary random methodology that isn't actually necessary for proving which numbers can or cannot exist, that numbers exist exclusively without being defined by dedekind cut.

Take for granted you'd been a retard, put it behind you if you can, then move on and demonstrate that infinity can be used as a number by giving me an example where invoking infinity as a number is otherwise understood to provide a sensible answer to an equation.

>>9578483
[math]\sum_{S}^{F} C[/math]

The Sigma E looking thing means this is a sum equation. C is a stand-in variable for the arithmetic to be calculated. S is the starting value, such as n=1. F is the limit, aka the finishing value. The summation is composed of partial sums where for every S incrementing to F, defines the amount of partial sums. The total sum and result of the equation is the sum of all partial sums.
[math]\sum_{n=1}^{5} 2n[/math] is the list of partial sums [math] \big( \stackrel{2×1}{2_{n1}}, \stackrel{2×2}{4_{n2}}, \stackrel{2×3}{6_{n3}}, \stackrel{2×4}{\8_{n4}}, \stackrel{2×5}{10_{n5}} \big) [/math], which is the same as 2+4+6+8+10, so the result of the sigma sum is 30.


[math]\sum_{n=1}^{x} \frac{1}{2^n}[/math] in this equation, x is a variable in place of where the limit is.

>>9578536
>If 1/inf = 0
>0×inf = 1
Wrong. You're multiplying by infinity, which is undefined.

>Division and multiplication aren't some abstract things, they're just glorified addition and subtraction.
They are will defined for finite numbers

>1/inf = 0 means if you have infinite 0s, adding them together equates 1, ergo 0×inf = 1
No it doesn't mean that. And adding infinite 0s is 0+0+0+... = 0. But this is not the same as multiplication by infinity, which is undefined.

>>9578609
Good fuckin job failing to use infinity as a number. Literally the only thing you had to do.

You are worthless.

>>9578576
>F is the limit, aka the finishing value
No, that is not what limit means in mathematics. Don't make up your own terms and expect people to know what you're talking about.

>>9578641
All of your issues stem from assuming that infinity must have the same properties as a finite number, when by definition it doesn't. So the failure is solely yours.

>>9578691
You backpedalling loser fucking retard kill yourself. You say that after going through all the trouble of providing for the construcyion of infinity as a number using dedekind cut.

Just fucking die you shameful piece of brainlet shit.

>>9578683
You too, you fucking die. If you're the same shitter then you've earned yourself two executions.

>>9578824
Not all numbers are finite. Learn how to read.

Daily reminder

https://www.wolframalpha.com/input/?i=infinity
An unbounded quantity greater than every real number.

>>9578970
I said
Demonstrate infinity as a number

Instead of doing this, you assume i think infinity is a real number, then change the discussion to that of infinity not being a real number

Why
Cause you are a retard
You can't demonstrate the usefulness of infinity as a number, so you change the subject. Three strikes, you're out.

>>9579074
>usefulness of infinity as a number
no one knows what that even means - because it's meaningless bullshit, just word salad

http://m.wolframalpha.com/input/?i=assuming%5Bx%3Dinfinity%2C+%28sum%5B1%2F2%5En%2C%7Bn%2C1%2Cx%7D%5D+%29+%5D

Also x<infinity

If multiplication is undefined for infinity, [math]2^(- \infty)[/math] is not 0, and the result is 1-undefined = undefined

Theres your infinite sum in action. Undefined.

>>9579152
[math]2^{ - \infty} [/math]

>>9579152

-2*inf=-inf
2*inf=inf
0*inf undefined

>>9579136
You're out. Get off the field asshole.

>>9579074
I've demonstrated it several times. For example the cardinality of a set is a number which describes the amount of members in the set. The cardinality of the set of natural numbers is countable infinity, also known as aleph null. The numbers that are used to measure cardinality are even called "cardinal numbers."

>>9579162
>i have no argument

>>9579152
>writing a bunch of shit to confuse wolfram alpha
You really are desperate huh?

http://m.wolframalpha.com/input/?i=sum%5B1%2F2%5En%2C%7Bn%2C1%2Cinf%7D%5D

>>9579167
You had multiple chances and blew them all
>>9579164
You stated a loose definition of infinity as a number using dedekind cut which by itself is useless as dedekind cut is not necessary for numbers to exist, what you didn't do is use infinity as a number to any degree, comprehensive or not, which doesn't solve the reason you replied being to demonstrate infinity as a number. Eat shit.

>>9579182
>i have no argument

>>9579173
It didnt confuse wolfram. 1-2^-x is 1-0 when 2^-infinity. It just reorders the logic expression which is that it's starting with the granted (1-...) which is where the real fuckup occurs. 1-0 = 1, but 1/2^n doesn't mathematically reach 1. This problem stems from the treatment of infinity as a number, where 1/infinity = 0 but so does every other number on n/infinity = 0, which just as clearly ought to mean 0×infinity could be any number and is undefined because it isn't any specific exact number, but it's any number inclusive of infinity, meaning there is only 1 value in this set of any values that suffices for 1-x=1 and its if n/infinity = 0*infinity = 0, yet infinite values for any other result such as if n/infinity = 0*infinity = 1 or 2 or 3 or any r wouldn't allow the result to equal 1, and all of this retardation stems from 1/infinity = 0 instead of any n/infinity being unknowable because infinity is not a number.

>>9579182
>You stated a loose definition of infinity as a number using dedekind cut which by itself is useless as dedekind cut is not necessary for numbers to exist
You are confusing necessity with sufficiency. The fact that infinity can be constructed as a number is sufficient to show that it is a number. But that does not imply it is necessary. Once again you fail at basic logic.

>what you didn't do is use infinity as a number to any degree
I mentioned several times the user of infinity as the cardinality of a set.

You lost on every front, even the irrelevant demand to "demonstrate infinity as a number." Even you know you lost. Stay mad.

>>9579225
>It didnt confuse wolfram.
It clearly did since it did not answer the question.

Keep writing these long posts of gobbledy gook, it's hilarious.

>>9579239
I can't have lost because you failed to demonstrate infinity as a number, which further wasn't even the point cause you're a dumb fag who cant read, the point was infinity by any and every definition is functionally useless and proveable as such using the very same arithmetic that often uses it, which does exist such as an infinite sum, which you were too retarded to realize its possible to demonstrate infinity as a number even though from ass to end this entire thread has been chock full of examples of infinity used as a number. You cant read, you can't do math, your grasp of the english language is foreigner-tier like some retarded ESL borderhopping mexican, you can't follow instructions because of your illiteracy, you're just fucking worthless. You know absolutely nothing of value and lack what constitutes the very basic notions of intuition, creativity, or intelligence. You are literally worse off for living than a $4 solar powered calculator.

>>9579245
>solves the question
>"didnt solve the question"
fucking YO, JOSE
GOOGLE TRANSLATE "RESULT"

>>9579262
>rambles incoherently like a bum masturbating on a bus back seat

>>9579267
>t. thinks tweets are too long, hasn't read a book since primary school

>>9579262
>I can't have lost because you failed to demonstrate infinity as a number,
But I did demonstrate it, and you did lose. Thanks for playing.

>>9577016
>How is arithmetic defined in the dedekind cuts construction?
If x is represented by the Dedekind cut X (I'm using the one-sided version for conciseness) and y is represented by the Dedekind cut Y then x + y is represented by the Dedekind cut [math]X + Y = \{x + y \mid x \in X, y \in Y\}[/math], i.e. the Minkowski sum of X and Y.

>Don't you need non-empty sets on both halves of the cut for this to be consistent?
The above definition works fine with [math]\varnothing[/math] and [math]\mathbb{R}[/math] as long as you're not adding together [math]\infty[/math] and [math]-\infty[/math]. So both [math]\infty[/math], both [math]-\infty[/math], one real and one [math]\infty[/math], one real and one [math]-\infty[/math] all work fine.

>Assuming we want to retain the properties of a field
That's one thing you do lose. [math]\overline{\mathbb{R}}[/math] is no longer a field.

>>9579264
That's not a solution to the question. The solution is 1 as shown here: >>9579173

>>9577997
>Tbh senpai the idea of dedekind cut doesnt really make sense by itself so extending beyond it isn't valuable.
It makes perfect sense. In fact, arguably it's the "canonical" definition of real numbers because it goes right to the very heart of what real numbers are: a Dedekind-complete ordered field. Dedekind cuts are the most natural reflection of this essential structure.

>>9579277
No you didn't. Quote the post where you did. If its any of the posts related to dedekind cuts, they're worthless first and foremost because dedekind cut is worthless first and foremost, but also because the definition of infinity derived from dedekind cut is not different than one of the first definitions from the start of the thread, that being "a number greater than all other numbers", which fails the most basic intellect test that there exists no greatest number. You did not demonstrate using infinity even once, you only attempted to define it, and even after your mind numbingly retarded failed attempt to define it in a different way than wasn't already assumed the most basic definition since the start of the thread, you continued to argue you did "demonstrate it" as if you dont know what demonstrate means. If i ask you to demonstrate a bicycle, that doesn't mean show me a bicycle, it means get on the fucking bike and use it, but you're evidently too retarded to know how to ride a bike so you're going to do everything but demonstrate how to use infinity as a number, much less how to use it under any definition.

Your dad should have fucking cum in your mom's mouth. You are an accident of existence.

>>9578238
>Dedekind cuts requires no set can be empty.
That depends on whether you want to deliberately restrict it to [math]\mathbb{R}[/math]. My point is that there is a very natural way to obtain [math]\overline{\mathbb{R}}[/math], from which [math]\mathbb{R}[/math] can be considered a restriction. More precisely, [math]\overline{\mathbb{R}}[/math] is just the two-point compactification or affine closure of [math]\mathbb{R}[/math].

>>9579282
i see, you really are retarded.

>>9579289
>my fantasy math
>fap fap fap fap fap fap fap

>>9578238
>>9579291
One way to think about this is to consider the different ways we can extend an existing mathematical structure to "close it" in some way:
[math]\mathbb{Z}[/math] is the closure of [math]\mathbb{N}[/math] under subtraction
[math]\mathbb{Q}[/math] is the closure of [math]\mathbb{Z}[/math] under division
[math]\mathbb{R}[/math] is the Cauchy closure of [math]\mathbb{Q}[/math]
[math]\widehat{\mathbb{R}}[/math] (the projectively extended real line) is the projective closure of [math]\mathbb{R}[/math]
[math]\overline{\mathbb{R}}[/math] (the affinely extended real line) is the affine closure of [math]\mathbb{R}[/math]
[math]\mathbb{C}[/math] is the algebraic closure of [math]\mathbb{R}[/math]

and so on. Each of these extended structures has their own useful properties.

>>9579317
Everything in this post except [math]\mathbb{R}[/math] is physically meaningless idiocy and has [math]\frac{1}{\infty}[/math] reason to exist. Enjoy becoming a professor and robbing your future students of success.

>>9579289
>If its any of the posts related to dedekind cuts, they're worthless first and foremost because dedekind cut is worthless first and foremost
Wrong.

>but also because the definition of infinity derived from dedekind cut is not different than one of the first definitions from the start of the thread, that being "a number greater than all other numbers"
So you don't know the difference between definition and construction. You don't really know anything about math.

>which fails the most basic intellect test that there exists no greatest number.
Wrong. There's is no greatest real number.

And you're ignoring that I showed you how infinity is a cardinal number, that it is used to describe the cardinality of the set of natural numbers. You didn't mention that because you know you lost.

>>9579341
Didn't mention it cause it has no real meaning.

>>9579339
>still no argument
Pathetic.

>>9579343
It's exactly what you asked for. Your entire argument is circular. You claim infinity had no meaning and your argument for this is to claim it has no meaning when meaning is given to you. You lose.

>>9579343
>>9579341
Also didnt mention the rest of your post cause it has no real meaning. I asked you to demonstrate infinity, you didn't. You still haven't. You have replied a dozen times and have failed to accomplish what you originally seemed confident you could succeed at.

Use infinity in a math equation.

>>9579351
Infinity has no meaning because the definitions for infinity insure it has no meaning by extension of using them.
As a singular number without relationship to reals (also a direction to never be reached, limitless, unending), an infinite sum cannot even arbitrarily increment to infinity. Any and all possible results can only be finite.
As a singular number with relationship to the reals, an infinite sum can arbitrarily increment to n, and the solution to the partial sum at n=infinity provides for no reasonable answer. If the sum is r/n, the infinite partial sum is 0 and is irrelevant to the total sum meaning n=infinity is irrelevant and summation finished prior to infinity in the reals, yet any real n doesn't equate the assumed result from convergence.
As a limitless set of a number with relation to the reals, n=infinity allows an infinite amount of 0s where any 0×infinity must only equal 0 else it is undefined, meaning the sum of all partial sums inclusive of infinite zeros is undefined.
As a

>>9579371
As a definition "greater than all real numbers", this would make it the greatest real number, yet no greatest real number can exist. There is no reason to assume this definition doesn't mean infinity isn't a real number, else it would have no relationship or reason to mention "real numbers". If you want infinity to be a number but not a real, what you want is to muddy the definiton of what numbers are, and what you need is to have infinity also have no relationship with real numbers. R/infinity = undefined, cause infinity is not a real number, unless you wish to attempt proving 0 is also not a real number.

Infinity doesn't exist. Sorry. You can't construct it without assuming it needs to exist, which is what happened with dedekind since infinity was already assumed to exist before his time. Usage of infinity as a direction of unending, a singular value, or innumerable values in a set, all the most popular ways of classically use it, can be extended to show infinity does not work as a number using arithmetic classically associated with infinity.

Infinity is a brainlet problem. You're a brainlet if you think it exists, cause that means you haven't even tried to prove it doesn't, even though if you tried to do so, you would figure out it doesn't work almost as soon as you started requiring very little brainpower at all. You lack the least bit of brainpower by continuing to assume infinity actually exists, much less is useful in arthimetic, because you only instead blindly believe it must be real instead of simply doing the math that clearly proves it's not useful.

>>9579385
>As a definition "greater than all real numbers", this would make it the greatest real number,

BS

if inf would be a real number it would, by definition, be bigger than itself
--> inf is not a real number

lrn2read

>>9579399
definition =/= construction

retard

>>9579400
Then it isn't a real number and therefore has no relationship to real numbers.

>>9579406
>no relationship to real numbers

https://www.wolframalpha.com/input/?i=infinity
An unbounded quantity greater than every real number.

>>9576381
At n=infinity, the sum would be a 1 with infinity zeroes after it.

The largest reasonable number is 1 with 27 zeroes after it. This is a million times larger than the value required to let everyone on earth have their own planet full of 7 billion people each, so everyone on earth would have a million planets each.

Accomplished with 1 and 27 zeroes

infinity is too big to be useful.

>>9579412
Then it is a real number because it as a relationshio to real numbers. You wanna be autistic or did you eant the definitiok to simply be "greater than any other real number"

>>9579427
>>9579400

>>9579427
>You wanna be autistic
if correct math is

>>9579429
"Greater than any OTHER real number" is explicitly non-inclusive of infinity.

>>9579433
the W-A link is there, use it

definition has no "other" in it

>>9579437
Alright, so it isn't a real number then. I was offering a better definition but you don't want it. Alternatively, it is a real number else there would be no reason to mention real numbers. You wouldn't say an apple is "a type of organism unrelated to crustaceans" or "a type of plant part related to fruit but not fruit even though you can eat it like fruit". If its relateable to real numbers, its a real number. If you think about it, it actually ought to be bigger than itself as that makes more sense in defining it, rather that it is a set of values that have order. If its just a singular value, it ironically loses accuracy when attempting to describe the amount of 9's in [math]\sum_{n=1}^{\infty} \frac{9}{10^n}[/math] versus the amount of 9's in [math]\sum_{n=1}^{\infty} \frac{99}{100^n}[/math] even though by partial sums it is quite clear that the second sum's amount of 9's is increasing at twice the rate of the first. Would you rather assume the second sum merely reaches infinity quicker then stops?

>>9579461
>you don't want it
nobody does

>>9579461
>If you think about it, it actually ought to be bigger than itself

this is when mathematicians know they have BS in their hands and throw it in the trash

Diameter of the universe is 91 billion light years
1 light year = [math]9.461×10^{15}[/meters]
Diameter of universe in meters is [math]8.60951 × 10^{26}[/math]
In planck lengths is [math]1.391296816×10^{62}[/math]
Plank length volume of the universe [math]1.410124806× 10^{186}[/math]
aka you need a 2 with 186 zeroes after it to describe every single possible part of existence in the known universe.

The collective partial sums of 2,000 from the infinite sum of [math]\frac{1}{n}[/math] means at that point where the sum is 2,000 the n value is 1 with 470 zeroes after it, which, which is [math]10^{284}[/math] times greater than every possible part of the universe divided into its smallest parts. Not 2 times greater, not a million times greater, not a trillion times greater, not a googol times greater.

a billion googols times greater than the universe divided into its smallest parts.

And this is still nowhere even close to infinity.

Infinity is needlessly big

>>9579494
>>9579499
So you assume the second sum's amount of 9's reaches infinity before the first sum's, then stops because it is a singular greatest value, therefore both sums have a singular infinite amount of 9's. One sum was infinitely larger than the other at a point, but now suddenly they each have the same value.

Real mathematicians would call you retarded. Pretty sure every teacher you ever had needed to have a private parent-teacher conference to discuss how slow you were.

>>9579502
>"640K ought to be enough for anybody."

>>9579516
>before
>numbers have wristwatches

what next, mustaches and sombreros?

>>9579519
2 with 186 zeroes after it lets you assign a unique number to every single planck length in the entire universe, with enoigh left over to assign half the universe's plank lengths a second unique number.

640k means you're desperately trying to strawman.

>>9579521
>numbers exist if humans do not
>humans dont have wristwatches
>time doesnt exist
You are the dumbest person alive.

>>9579525
1/(2 with 186 zeroes) > 0
it's useless

>>9579528
ayyy caramba

>>9579532
>the smallest possible thing is bigger than nothing
Tell me more about this exciting daring find of yours.

>>9579534
Good job turning into a mexican to prove the point numbers are mexicans.

>>9579536
>the smallest possible thing
you touch it alone in the dark

>>9579546
I'll have you know my dick is 9 inches you sad bastard full of nothing but ad hominems. Wanna know what isn't an ad hominem?
YOU CAN'T DO MATH
YOU ARE ILLITERATE
these are truthful. You've proven it true in all your posts, archived for eternity.

>>9579555
was talking about your brain

>>9579558
>y-you touch your brain
>i-i was only pretending to be retarded
Thats going in the archive too.

>>9579562
fyi, your brain is a pimple on your dick

You ought to have realized it by now but I get off on proving you wrong, and i'll do it until you no longer exist.
You don't need to exist, remember that. Your existence relies on trying to prove otherwise or accepting it. Both end in death.
I killed you just in time, and we don't even need to go through the rest of time to prove it. Humans were a mistake.

>>9579573
you most certainly are a mathematical wiz-tard

>>9579502
>Diameter of the universe is 91 billion light years
Wrong.

>>9579968
observable universe
93 bn ly