/sci/ - Science & Math

>>9733681
Geometric series are used in the proof of the Banach fixed point theorem, which in turn is used to prove the existence and uniqueness of solutions of differential equations with initial conditions, which are used all the time in physics and engineering

>>9733681
Show me with a pen and paper where there's a difference between these numbers. Draw me two different circles.

>>9733681
Well, the formula for the sum of a geometric series would be wrong, that's relatively big.

No math is based on this.

0.999... is a notation for the decimal expansion of the number 1.

To say that any math is based on a chosen notation is akin to say that any math is based on giving the number 1 the name "one".

U are amazing maaan

>>9733681
Is there any math based on the fact that 1/5 = 0.24972497... ?

In base 12.

>>9733681
Two real numbers are different if and only if there is another number strictly between them.

However your equation is false in surreal number set.

The only nonsense here is your own ignorance.

>>9733681
Talked about how this caused major bs in modern (((science))) in this video
https://www.youtube.com/watch?v=KoELwBYzNDY

>>9734093
>set
*class

>>9733687
literally has nothing to do with what op asked

>>9733681
but it is correct
[math]0.\dot{3} \times 3 = 0.\dot{9}= \frac{1}{3} \times 3 = 1[/math]

>>9733690
I can't.

>>9734964
>elementary proof without any reference to more advanced topics such as series, limit, formal construction of reals numbers, etc
>a proof is elementary if you use all the underlying shit implicitly
What did wikipedia mean by this?

>>9734515
how do you multiply infinite 3's?
can you show that to me?

>>9735008
3*0.3... = 0.9,,,

>>9733681
There was a fucking retarded thread about this and infinity literally yesterday, at this point this topic is as dumb as climate change denial, evolutionary x, and IQ threads.

0
OKay...

0 ≠ 0.0
What is he doing?

0 ≠ 0.00
No, go back!

0 ≠ 0.000
Is that even legal?!?

0 ≠ 0.0000
Holly shit nigga, that's fucked up!

0 ≠ 0.00000
Wtf. Don't make me call your mom!

0 ≠ 0.000000...
How can you sleep at night?

Numbers are fake

>>9733681
it's literally just a property of the real numbers, you faggots

shut up already

>>9735022
No fuck you, fuck you all.
I don't care if its true or not, I don't want to know your arguments for or against it.
I want to know if there are mathematical concepts that rely on 0.999 = 1 being true. If there are, I want to know what they are called and I'll do the rest of the research myself.

>>9734964
>proof
lol

>>9735282
The construction of the real numbers as cauchy sequences. You could also say if that isnt "true" our notions of general convergence would fail horribly if they didnt work for such an easy example. Though, that a number can have different nuneral representations even if you take the same basis is really nothing that important, nor it isnt contriversial. The thing to understand is that formally that makes no sense because an infinite series isnt regarded as an actual infinite sum, doing that is called the generality of algebra which caused many problems until cauchy and weirstrass formalized the notion of convergance, which roughly means that you define a sequence of partial sums 0.9 0.99 0.999... And you can gind that by taking arbitrarily large elements of the sequence you can get arbitrarily close to 1. See delta-epsilon definition of a limit. So you say, o okeyz this series converges to 1, so you can absue notation and say 0.9999... Is 1, but not really, as the infinite sum is not defined.

>>9735398
Nor it is controversial*.

>>9735282
>mathematical concepts that rely on 0.999 = 1 being true
Consider an interval
[eqn]\theta\,\in\,[0,\pi]~~.[/eqn]
What is the length of the interval? It's [math]\pi[/math] obvioulsy.
Now, consider an interval
[eqn]\theta\,\in\,[0,\pi)~~.[/eqn]
What is the length of the interval? It's still [math]\pi[/math] because [math]0.999...\,=\,1[/math]

>>9735402
I should say, "It's still pi *in the framework* where 0.999...=1"

Hey i was just thinking about posting this.

this video gave a good reasoning for why 0.999... =/= 1. https://www.youtube.com/watch?v=--HdatJwbQY&t=4s

if 0.999... is equal to 1, then limits are harder to do because 0.999.. is the closest number to 1 without being one.

>>9733681

It is utter bullshit, and papers over the fact that current maths is hogwash.

Some day in the future people will look back at this shit and laugh with derision.

Student: "How the fuck did they work with that crap?"

Teacher: "Hey don't be too harsh on them, did you know that for a long time they had no concept of zero until the Babylonians introduced the term."

Student: "Oh lol! But they still put up with that crap when it was more than obvious that something was fundamentally wrong?"

Teacher: "Not only did they put up with it, but there were many people who defended it! Just like people opposed Darwin's theory of evolution for many years, and called him a crank!"

Student: "But I don't understand, it was so obviously wrong, why work with a system that had such fundamental flaws?"

Teacher: "Well, it was just what they knew at the time and they hadn't reached the conceptual understanding that we have today, thanks to the breakthroughs in mathematics which occurred in the 23rd century. Think of it this way, the Romans did pretty well with their archaic numerical system, it worked for them, well, in the same way the old system worked for the people of the 21st century."

Face the facts. You fuckers who defend this shit are going to be seen as the dinosaurs of maths. Bet you will all remain plenty quiet when this crap is finally overthrown and revealed for the illogical bullshit it is. But more likely you will say " I always suspected there wasn't something right about the maths of my day." You fuckers.

>>9735494
>disregards infinity

>>9735494
>that reddit spacing
It's shitty latex guy again, don't you ever give up?
Now you're writing plays about your bullshit?
Take your pills.

>>9735488
>extremefinitism.com
Who sponsors them, the flat earth society?
You're not welcome here, crank.

if 0.999... = 1, then what about a number infinitely close to 0.999... like 0.999 but with an 8 at the end. If you subtracted 0.999... and 0.999...8, it would be the same difference as 0.999... and 1 which is 0.0000....1.

also if you used the same algebraic method for a number infintely large instead of small like ...9999.0 you'd get -1

...9999 = X
...9990 = 10x
x - 9 = 10x
-9 = 9x
-1=x

Using that algebraic method you'd get 1 = 0.999... AND 1= -1

>>9733681
[eqn] \sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6} [/eqn]
>this kills the finiautist.

>>9735521
>number infinitely close to 0.999...
No such number exists by the Archimedean property of [math] \mathbb{R} [/math].
Maybe in alternative number systems

>>9735518
doesn't matter who it came from. just the argument.

>>9735521
Your post demonstrates why you shouldn't play fast and loose with infinity. That's why modern math requires rigor. [math] 0.\bar{9} [/math] is unambiguously defined as follows:
[eqn] 0.\bar{9} \equiv \sum_{n=1}^{\infty} \frac{9}{10^n} = \lim_{k \rightarrow \infty} \frac{9}{10}\frac{1-\frac{1}{10^k}}{1-\frac{1}{10}} = \frac{\frac{9}{10}}{1-\frac{1}{10}} = 1 [/eqn]
Where the triple equals indicates a definition (so it cannot be argued with).

>>9735539
>cannot be argued
everything can be argued with

>>9735549
If you deny this definition you're no longer working in [math] \mathbb{R} [/math], nothing wrong with that, it just so happens [math] \mathbb{R} [/math] is one of the most useful number systems.

>>9735549
https://www.tfd.com/succesfully

>>9735539
You mean modulo

>>9735553
>equivocation fallacy
Symbols have multiple definitions, i chose to define my triple bar to be a definition symbol. Symbols are arbitrary as long as they're consistent.

>>9735558
>using nonstandard notation on an elementary proof

>>9735560
Triple bar for definitions is extremely common fucktard, it's literally given by \equiv in latex

>>9735521

where did you get 1 = -1? you've shown that ...9999.0 = -1, but I don't know how you get from there to 1 = -1 given that ...9999.0 is not 1.

>>9734148
>Too much of a brainlet to see the connection between decimal expansions and geometric series

>>9735494
>You fuckers who defend this shit
The ONLY reason I am defending it is because it is the best thing we got, construct something as powerful as analysis in a finitist (or whatever) way and I will abandon real numbers in a heartbeat.
But the only thing you will do is complain and complain, without even suggesting an alternative.

>illogical bullshit
You clearly missed the first lesson in mathematics.
For all we know ZFC is perfectly consistent and everything in math is entirely logical.

>>9735494
Provide a proof that .999...=/=0 or GTFO. In math you're not allowed to be a contrarian just for lolz.

>>9734148
lol virgin nomaths detected

>>9736373
That's an elementary proof that you should have learned in calc 3

>>9735521
anything after the ellipsis is =0 and can be ignored, since 1/inf=0

> If you subtracted 0.999... and 0.999...8
same as 0.9... - 0.9... = 0

>>9733681
[math]0.999\dots = \sum\limits_{i=1}^\infty 9\times10^{-i} = 1[/math]

>>9736469
OP either means something entirely different by his "0.999...", or he has no idea whatsoever what he means by it. Probably the latter. And use lower ellipses, please...

>>9735521
A number that's infinitely close to 0.999... is 0.999... by definition

>>9735521
...999.0 is not a number. There is no infinitely large real number

>>9736547
Its a number derived from mistakes in evaluation. Such as 1/9 = 0.111... × 9 or 1/3 = 0.333... × 3

The very method of getting any repeating decimal creates an innacurate approximation factor, so as long as people continue to evaluate [math]\frac{1}{3} = 0.333... \text{ instead of } \frac{1}{3} \approx 0.333[/math], theres going to be a lot of retarded efforts going forward.

The problem here is that the notation simply needs to be altered or extended, such as in [math]\frac{1}{3} = 0.\bar{3}_{\frac{1}{3}}[/math] where we can retain equality, a decimal interpretation, as well as a source vector attributed to the evaluation. It's like an alternate form of remainder representation, but [math]\frac{1}{3} = 0.\bar{3}r1 × 3 = 0.\bar{9}r3 [/math] doesn't really indicate what to do with the remainder while contrarily, [math]0.\bar{3}_{\frac{1}{3}} × 3 = 0.\bar{9}_{\frac{3}{3}}[/math] allows the reminder to be understood, and that whole 3/3 then becomes a rightmost value of 1 to be added to 0.999..., which solidly adds up to 1.0 total.
[math]0.\bar{9}_{\frac{3}{3}} = 0.\bar{9}_{1} = 0.\bar{9}_{\stackrel{\leftarrow}{1}} = 1.0 \\ 0.999...99[9+1] [/math]

It's not exactly casio calculator friendly notation, but we don't exactly use casio calculators anymore anyway. Something's got to change to get away from infinity being treated in math as a sensible number value when everyone already knows it isn't.

>>9736606
0.333... = sum from k=1 to inf of 3(1/10)^k = 3(1/10)/(1-1/10) = 1/3

Can you define a base whee you don't get repeating somthing like .999... = 1. like

>>9736620
Infinity isn't a number.
Its not an amount or a size. There is zero intelligible sense in setting your iteration limit to infinity. You're also confusing convergence for equality.

>>9736606
this batshit crazy ranting with kindergarten doodles, in every thread...
get a life

>>9736627
>Its not an amount or a size
go fuck yourself

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

>>9736626
Base-infinity

aka unresolved fractions.

>>9736632>>9736629

>w-wolfram s-says its an amount s-so it must be true...!
Yea?
It's a quantity, is it?
What number is it then.

>>9736635
it's not a real number - can't you read?

>>9736606
No you're just retarded

Say you got ten squares. The tenth one is split into ten. One of those tenths is tenthed. One of those tenth is tenthed. Onto infinity. All squares are filled in. You could notate this 9.999... or 10. It makes no difference.

But oh infinity doesn't exist fuck you

>>9735008
3 * 0.3 = .9

[math] 3 \cdot \sum_{ k=1 } ^n \dfrac { 3 } { 10^k } = \sum_{ k=1 } ^n \dfrac { 9 } { 10^k } . [/math]

[math] 3 \cdot \sum_{ k=1 } ^{ n+1 } \dfrac { 3 } { 10^k } = \sum_{ k=1 } ^{ n+1 } \dfrac { 9 } { 10^k } . [/math]

now take the limit as n goes to infinity of the sum.

>>9736639
Are you retarded? Assuming the splitting method removes nothing from the squares, the volume of the initial 10 squares is preserved throughout. It is literally NEVER 9.999...

>>9736627
>Infinity isn't a number.
Wrong. https://en.wikipedia.org/wiki/Cardinal_number

>There is zero intelligible sense in setting your iteration limit to infinity.
Wrong. It's well defined, very useful, and consistent.

>You're also confusing convergence for equality.
An infinite sum is equivalent to the limit by definition.

>>9736639
>doing something infinitely

>>9736647
>the volume of the initial 10 squares is preserved throughout.
Yes it's always 9.999...

>>9736637
But quantities can be represented by numbers.

So if it's not a number, it also can't represent a quantity.

Connect the dots with a straight line between (0,0) and (1,0). This isn't novel thinking or rocket science. Use your brain.

>>9736649
There is an infinite amount of stupidity in your crapposts

>>9736652
do you have a brain tumor or something?
your posts are cancer.

>>9736655
That is a number it's (1,0)

>>9736655
It is a number, which represents quantities like the cardinality of the natural numbers. You are confusing real numbers for all numbers.

By the way, how do you construct the reals?

>>9736656
Glad to know there is no existing amount of retardation in my posts.

>>9736662
You construct real numbers with the symbols 012345678 and 9

You don't need an autistic method to define a number you gullible retard.

>>9736667
Why? Because you said so? Why should I trust a retard on the internt over wolfram alpha?

>>9736667
>You construct real numbers with the symbols 012345678 and 9
No, you don't.

>>9736668
Why should you trust wolfram alpha?

>>9736667
So you can't even construct the real numbers yet you think infinity isn't well defined? LOL.

>>9736669
I guess 453 isn't a real number then.
You sure showed me.

>>9736678
You don't have to trust wolfram alpha, just read the proofs.

>>9736682
>I guess 453 isn't a real number then.
That is a logical fallacy of enormous degree.

>>9736686
You're confusing proof for "something that exists". I don't doubt you can find arrangements of words and evaluations which have lead you to believe what youbl believe, but that doesn't mean lying doesn't exist, and it doesn't mean a tumblrette's blog about transgenderism is somehow proof of anything.

Things exist. Get over it.

>>9736687
You're the one who doesn't believe real numbers are constructed with the ten arabic numerals. We can extend this to other number writing systems but if literal common defacto arabic numerals are confuzzling you then there's no real good in expanding upon the base.

>>9736695
>You're the one who doesn't believe real numbers are constructed with the ten arabic numerals.
The base is entirely irrelevant to the definition of the reals.
You can use whatever base you want, it is just a way to describe something.

See: https://en.wikipedia.org/wiki/Real_number#Definition

>>9736700
I challenge you to create a number that isn't a real number while using the arabic numerals, via your interpretation of real number construction.

Go.

>>9736704
To be clear, ONLY arabic numerals.

>>9736690
>You're confusing proof for "something that exists".
What does existence have to do with mathematics?

>I don't doubt you can find arrangements of words and evaluations which have lead you to believe what youbl believe, but that doesn't mean lying doesn't exist, and it doesn't mean a tumblrette's blog about transgenderism is somehow proof of anything.
There is no belief in mathematics. The results of proofs are objective truths, there is no way to get around this.

>>9736704
This doesn't make any sense.
The arabic numbers are arbitrariy symbols in an arbitrary basis.

Read the wikipedia article.

>>9736709
[eqn]\sum_{n=1}^{\infty} \frac{9}{10^n} = 1[\eqn] is not objective truth you fuccboim

More than that, it invokes multiple objective fallacies.
[math]\infty[/math] is not a defined number value so you can't increment to it, and the sum of partials sums up to ANY given n is solely just a string of 9's.

Wheres your objective truth. What fucking truth do think this is. It's an objective lie and nothing but. It is proveably false by the defacto history of basic arithmetic preceeding calculus and the history of basic arithmetic after calculus.

You unironically could not be further from the truth.

>>9736714
Lets recap.
Your claim:
>need arbitrary methods to "construct" real numbers and real numbers dont exist without these arbitrary methods
Your proof:
>????

My claim:
>real numbers are constructed from numerals
My proof:
any combination of numerals creates a number that is verifiably real under your autism methods.

now bring it down to occams razor. Do we need to teach children cauchy dedikind garbage, or do we need to teach them 1 through 10.

>>9736725
>>need arbitrary methods to "construct" real numbers and real numbers dont exist without these arbitrary methods
>Your proof:
I linked to the wikipedia article containing the proof.

>any combination of numerals creates a number that is verifiably real under your autism methods.
Prove that sqrt(2) can be expressed that way.

>>9736726
do you believe the square root of 2 cannot be represented by numerals.

are you for real right now dude.

>>9736736
>do you believe the square root of 2 cannot be represented by numerals.
I asked for a proof (I have one using "my" definition of the reals).
Can you prove it or not?

>>9736718
It is. It's proven by the definition of the infinite sum and the theorem of convergence.

>[math]\infty[/math] is not a defined number value so you can't increment to it
Wrong. See the definition of the limit: https://math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/SandS/lHopital/define_limit.html

The infinite limit is simply the bound of all of a function's output no matter how large the input.

>and the sum of partials sums up to ANY given n is solely just a string of 9's.
Wrong. Any string of finite n 9s is equivalent to a string of n-1 9s followed by an 8 and then infinite 9s. So it's not solely a finite string.

>Wheres your objective truth.
It's right there for anyone to see and anyone to disprove. So far you have attempted and failed, only succeeding at proving your ignorance.

>>9736743
whether or not you want to trust wikipedia, the square root of 2 has been rendered as an approximate numeral for nearly 4000 years.

Do you think the babylonians had difficulty determining what is or isn't a real number?

>>9736718
>Wheres your objective truth.
Mathematics can not possibly contain objective truths.
Everything only has truth value in relation to the axioms.

>>9736744
>Any string of finite n 9s is equivalent to a string of n-1 9s followed by an 8 and then infinite 9s. So it's not solely a finite string.
your mother should have swallowed.

>>9736747
>approximate
You were asked to express sqrt2, not an approximation

>>9736752
>your mother should have swallowed.
He is right according to the standard definition of the real numbers.

>>9736752
So you have no arguments left. Thanks for admitting 0.999... = 1

>>9736756
Sure senpai i got this

Sqrt(4) = what number times itself equals 4. Oh shit nigga that 2.

Sqrt(2) what number times itself equals 2
hm.. can't be 1.. can't be 2... gotta cum betwixt 1 and 2. Is it 1.5?
Lets see. 1.5×1.5 = 2.25
Nope
1.4?
1.4 × 1.4 = 1.96
So its between 1.4 and 1.5
Is it 1.42?
1.42 × 1.42 = 2.0164
how about 1.41
1.41 × 1.41 = 1.9881
So its between 1.41 and 1.42
Is it 1.415?
1.415 × 1.415 = 2.002225
Hm.
1.414 × 1.414 = 1.999396
so its between 1.414 and 1.415

ya know, i think i might be onto something. I could do this indefinitely for as much accuracy as i want.

Woah.

>>9736759
Can't argue against inbred tardation that thinks infinity is a number amount. Doesn't require an argument, just requires locking you up in an asylum.

>>9736772
I still don't see an expression. How long before you get to sqrt(2)?

>>9736782
Are you challenged?

>>9736777
>Can't argue against inbred tardation that thinks infinity is a number amount.
Yes, apparently you can't argue against it since you continue to avoid responding to >>9736648

>>9736772
Don't you feel embarrassed?
I asked for a proof that sqrt(2) can be expressed as a sequence of Arabic digits and you got is:
>so its between 1.414 and 1.415

This means nothing, this doesn't prove what I wanted you to prove in the slightest...

>>9736784
Oh infinitely long. OK.

>>9736784
Can you actually provide a proof?
Mayb

>>9735521
>like 0.999 but with an 8 at the end.
The 8 at the end means the expansion ends, thus it's not "like" .999...
You didn't provide a contradiction, you just showed that you don't understand infinite decimal expansions.

>>9736373
>Provide a proof that .999...=/=1
Fuck me and fuck typos :(

>>9736786
I said i could continue. You could continue it yourself though. Its pretty basic arithmetic.

Do you think irrational numbers aren't real numbers or something?
Or do you think you somehow understand the square root of 2 with umlimited arbitrary precision? Cause the limit is only 10 trillion digits as of 2016. If you got a method to know every digit without calculation, that'd be very impressive! More than the sqrt(2), you would also have knowledge that P = NP!

share your amazing knowledge with us.

>>9736786
Nobody can write out infinite digits, but that doesn't mean it doesn't exist. In fact, the fact that you can write it out with arbitrary precision means that it must be infinite. And he did give you an algorithm for finding sqrt{2} with arbitrary precision.

>>9736802
>I said i could continue.
Utah but how long do I have to continue for to get to sqrt(2)? 10000 decimal places?

>>9736802
>I said i could continue.
Which isn't a proof whatsoever.
Please give me the proof.

>Do you think irrational numbers aren't real numbers or something?
According to your definition I don't know.
You haven't showed that sqrt(2) is a a real number assuming your definition.

>Or do you think you somehow understand the square root of 2 with umlimited arbitrary precision?
No, does that prevent you from proving your claim?

>>9736804
>Nobody can write out infinite digits
I didn't ask to write out all digits I asked you for a proof that you COULD write them out.

>And he did give you an algorithm for finding sqrt{2} with arbitrary precision.
Irrelevant to the claim he should have proved.

>>9736784
>Is asked for an exact expression.
>Gives an approximation, twice.
>Has the nerve to call anyone else retarded.
Why do you embarrass yourself so?

>>9736498
oh sorry about that.
I didnt realize

>>9736802
I have a feeling he meant to talk about sqrt(-1)

>>9736815
No, I absolutely didn't.

>>9736635
>1514403883630.jpg
oh my god, it's you again. Nobody will listen to your doodles here, child. While you sit around with your finger in your ass like the Neet dropout scum you are, pure mathematicians are using infinity and other abstract constructs to pave the way for the applied mathematicians and scientists, which is why you can shitpost on a computer in the first place.

>>9736817
Well then you're going to have to let us all in on whatever goofy logic you're attempting to arbitrate by, or simply fuck off.

>>9736802
There are formulas to calculate [math] \sqrt{2} [/math] with arbitrary precision.

>>9736824
I'm a programmer you dumb fucking retard. I am fully aware of real math with real applications. Fucking none of it involves infinity.

>>9736825
A guy claimed that the real numbers could be constructed by writing down Arabic digits.
I asked him to prove that sqrt(2) was in fact such a real number, something supposedly rather trivial.
All I got was an approximation and name calling.

>>9736827
I gave you one of them in brute force, so what.

>>9736831
The argument was you can construct a real number from numerals. If you think 1.4142135623730950488 isn't numerals, or if you think 1.41 is less of a real number than 1.414213, thats all on you and irrelevant to the claim.

>>9736828
>I'm a programmer
AHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHA
You already have a board you braindead code monkey
>>>/g/
Also I'm a pure mathematician but I'm pretty good at programming too, you can learn more than one thing you know.
>I am fully aware of real math with real applications
HAHAHAHAHAHAHAHAHA
It's a fucking tragedy that schools are letting CS people graduate without calculus, it's making fucktards like you think they're smart, assuming you even have an education beyond a code bootcamp or some books you read on your own.

>>9736836
Provide a snippet of pseudocode utilizing infinity. Feel free to reference a library or package if you need it, i'll gladly look it up to double check.

Do it nigger. Don't run, don't change the subject, don't move the goalposts. Utilize infinity in code.

Do it.
Do it now.

>>9736834
>The argument was you can construct a real number from numerals.
Exactly that is what I said.

>If you think 1.4142135623730950488 isn't numerals, or if you think 1.41 is less of a real number than 1.414213, thats all on you and irrelevant to the claim.
All that is irrelevant.
Prove that sqtr(2) is such a number.
1.4142135623730950488 is one, I grant you that, but 1.4142135623730950488 isn't sqrt(2).

So please where is the proof?

>>9736842
Do you understand that infinity is abstract and any mathematician will agree you can't write a finite string of 9s that reaches infinity. Do you realize infinity is just a useful abstraction that allows us to find good approximations and other things, and throwing it out would make applied mathematics way harder? Perhaps mathematicians are agreeing with you more than you think, there's no need to argue every day.

>>9736842
Computers can't deal with infinity in the way you want, but it can manipulate it symbolically. Unfortunately for you that fact is immaterial to the identity [math] 0.\bar{9} = 1 [/math].

>>9736846
[math]\sqrt{2}[/math] is not a number you idiot. It is an expression. What the fuck, is this the retarded shit you've been pulling this whole time? Honestly?

you may as well have just been saying "2 + 2" isn't a number.

Goddamn motherfucker literally WHAT are you doing with your life.

>>9736856
>2√2 is not a number you idiot. It is an expression.
No. sqrt() is a function, I want to evaluate the function at a certain point.

>What the fuck, is this the retarded shit you've been pulling this whole time?
I want a simple proof, can you do it?

SPOILER: you can't.

>>9736856
>>9736859
>reddit spacing

>>9736802
>I said i could continue.
Let me prove sqrt(2) is rational.

I obviously can approximate it arbitrarily well with rational numbers. QED.

>>9733681
[math] 0.999.... = \frac{9}{9} = 1 [/math]

I mean are you fucking serious? This is elementary school tier shit. Fuck off OP.

>>9736859
Give me your proof your goofball. If your next post doesn't include your method you've decided to arbitrate by, you forfeit your argument by default.

>>9736865
What grade of elementary school wete you in when you learned 9÷9 = 0.999...

>>9736866
>Give me your proof your goofball.
A proof for what?
Which claim am I supposed to prove, you have to tell me that first.

>>9736872
you just forfeit your argument by default.

>>9736867
It's 9 for every number that repeats in the denominator and the numerator is the number that repeats.
Is American education THAT bad that you don't know this anon?

>>9736874
I couldn't prove a claim which never was given to me...

But I assume the poster who still hasn't proved that sqrt(2) is a real number has lost his argument some hours ago, so fine.

>>9736882
Your position has been forfeit my man. The discussion is over. You were called out for wasting everyone's time with your brainletism. You wont be getting another reminder.

>>9736867
Oh look, another baby scribble from our resident code monkey, so cute.
Now back to work monkey, your boss needs that java app by tomorrow.

>>9736888
Okay, thank god my opponent lost 20 posts before me.

>>9736867
>using obelisk for division ever
this is an 18+ website

>>9736842
github.com/kokke/tiny-ECDH-c/blob/master/ecdh.c is a code to compute the Diffie-Hellman key agreement algorithm, and it references infinity explicitly. As you would expect, since every elliptic curve has an infinity point.

>>9736920
He'll ignore this post, as usual.

>>9736606
[math]A: \frac{7}{22} = 0.3\overline{18}_{\frac{7}{22}} \\ B: \frac{7}{9} = 0.\bar{7}_{\frac{7}{9}} \\ A+B = 1.0\overline{95}8_{\frac{217}{198}} = 1.0\overline{95}8_{1 \frac{19}{198}} = 1.0\overline{95}_{\frac{19}{198}}[/math]
It just works

>>9736920
Nope.

>>9736959
LMAO
the code monkey doesn't even understand elliptic curves
HAHAHAHA
go make a java app pajeet

>>9736932
He could learn more on rosettacode.org/wiki/Elliptic_curve_arithmetic if he would care to bother, which I doubt. But I will go to bed now and hope to come back to a dead thread tomorrow morning.

>>9736842
>do this thing i asked
>>9736920
>does the thing
>>9736959
>Nope.

>>9736932
It is doubtful that he can even read code.

>>9736981
Of course, it's not a trivial app written in Java so the monkey can't understand it

>>9736972
if you knew about computers, you would know that an infinity reference in code is not actually infinite.

so did you know that or not?

>>9736972
I'll assume you didn't know it.

https://www.openprocessing.org/sketch/549665

>>9737078
>>9737105
Lmao idiot
Leave the math to the adults, your deadline for your corporate overlords is coming up fast.
stupid finiautist pajeet
>he doesn't even understand elliptic curves
>he doesn't even understand computers
>he's so autistic that he thinks math is a conspiracy
>>>/reddit/

>>9737165
Feel free to tell me if something is wrong with the code.

>>9737254
>infinity is finite because muh code says so
retard alert

>>9737254
>infinity equals 1.8 x 10^308 because that's the largest number a double precision float can hold
you can't be this dumb, it's just not possible.
What about quad precision? What about arbitrary precision packages?

>>9737254
>a number has to be computable to exist
retard
http://mathworld.wolfram.com/ChaitinsConstant.html
didn't they teach you this in CS class?
or are you a software """"""""""""engineer""""""""""""

>>9737296
Every example in the provided links that aimed to implement infinity were using a built in storage type. Regardless if its float or double, POSITIVE_INFINITY is equal to a real finite number in these examples.

Kys any time.

>>9737360
Infinity as implemented in your brainlet programming "languages" is not related at all to the abstract mathematical concept of [math] \infty [/math].

>>9734515
But this implies .333... and .999... are part of a whole number, its not. Fractions are used as whole approximations of decimals or really small numbers.
.333...+.666... would equal 1.222...

>>9737391
lmao 10/10

>>9737386
That wasn't the point of this conversation.

>>9734964
Wouldn't simply showing the geometric series be even more elementary than this long winded description which barely makes sense.

>>9737397
I think you and the math anons are talking about different things. Of course you can't count to infinity, but working with infinity in an abstract way is very useful, ask your engineer friends. Math isn't concerned with reality, your views of the physical world are compatible with the mathematical notion of infinity. So we agree, can you never post about this shit again? Infinity can both not exist and be useful.

>>9735282
Limits are vaguely connected to the topic. Looking at some limits of lots of different functions might prove it to you.

>>9737405
It isn't useful bruh.

Daily reminder that 0!=1

>>9737418
It's pretty useful. Limits make a lot of things that can be done with finite methods easier. Engineers still use limits and stuff when they have analytic functions for their applications, like a polynomial that's been fit to a set of data. Limits are inherently "infinite" but they don't involve counting to infinity, so you can accept them while still staying consistent to your philosophy.

>>9737419
yes, 0! = 1 and 0 != 1.

>>9737419
>he doesn't work in fields of characteristic 1

>>9737313
A number has to be real to exist. We can come up with plenty of numbers larger than [math] 2 × 10^{308}[/math] that wont naturally compute on solely built-in data types, and they're obviously real, but that's not the point. The point is that built-in data type enumeration has some maximum finite values, and the arbitrary problem is that the maximum possible value in these data types is communicated as "infinity", even though its just a real finite number that can be incremented to unlike the mathematical fantasy depiction of infinity. It's not wrong to say its unrelated from the maths infinity, but it's not right to say it has some definite uses either. Practical maths applications in computing doesn't utilize infinity the way pure maths students seem to believe it would or should, and it's not necessarily because a memory address storing a data type number only has so many bits to work with that will obviously overflow if enumerated upon too much, but rather because infinity is not well defined in a real physical space and can't be represented by a configuration of intelligible bits. It isn't well emulated or adapted because it is vaguely used and vaguely defined in maths, where the only real problem in all of this is that mathematics references infinity in a way that is not actually constant or intelligible. The calculators aren't wrong. The math is wrong.

>>9737455
Something doesn't have to exist to be useful. Something doesn't have to exist to be well defined. Infinity is consistent in that if you assume certain things then you don't come across contradictions. It is not vaguely defined unless you choose to define it vaguely. Mathematicians are very careful to be explicit about their intentions.
So infinity doesn't exist, but it is useful, consistent (insofar as we let it be), and allows us to perform more complicated mathematics with symbolic calculations which are barely even numerical. Math isn't just numbers. These symbolic calculations may seem like navel gazing nonsense but people have found applications for even the most abstract of mathematics (see number theory, the foundation of modern cryptography).

>>9737455
and the identity [math] 0.\bar{9} [/math], obviously does not mean we can produce a string of 9s with a computer such that they reach 1, it just means that if we assume infinite decimals can exist, then for that system to be consistent numbers must have multiple representations. Any mathematician will agree that a computer cannot verify that [math] 0.\bar{9} [/math] in the way that you're arguing it ought to for us to say it's correct.

>>9737462
What assumptions are you making about infinity if you aim to assume infinite decimals can exist?

What assumptions are you making about the ability to enumerate through infinite decimals if [math]\frac{n}{\infty}[/math], the smallest part of enumeration in infinite arbitrary accuracy, is null and not an enumerable value? How do you get from 0.9 to 0.99 when that second 9 of infinite 9's can't have come since 0 incremental shifting occurs in the smallest part of infinite decimals, which primarily means no shifting may occur if any requires even a multiple of the smallest part that is nothing ever but 0?

If [math]\frac{n}{\infty} = 0 \\ 0 × n = 0 \\ 0 × \infty = n[/math]
Then this not a number or a quantity or a size or a value or even a vector or commamdable direction to do work unending; no, it's really just a boolean. Theres two positional states an enumerable value can have in relation to infinity, and they're just evaluating whether the number is or is not infinity. There is no degree of infinite'ness, bo spectrum of values closer to infinity than others - its just real or infinite, black and white.

So we really can't be referencing infinite decimals can we.

it's just that
[eqn] 0.\bar{9} \equiv \sum_{n=1}^{\infty} \frac{9}{10^n} [/eqn]
and that sum converges under the standard axioms. You can do non-standard mathematics but we use these axioms for a reason, you can do a lot of useful stuff with the axiom of infinity. You're arguing philosophy, not math. That's fine and all but neither you nor mathematicians are really "wrong".

>>9737482
And the important thing is that summation definition allows you to turn any repeating decimal into a ratio of integers (since all infinitely repeating decimals are rational), so basically you can do some calculations where the calculator says 1/3 = .33333333 or whatever, and then you can turn your end result, if it's repeating, back into an exact fraction using the summation. Is that not useful? This very definition allows us to avoid ever actually invoking infinite decimals, that should be a good thing under your philosophy.

>>9737489
Less philosophy and more morality. I don't believe it's moral to teach the treatment of infinity, because it is in actuality functionally incorrect. Its immoral to teach objectively useless information while portaying it to be useful. The existence of infinity in maths leads to truly asinine and puzzling worthless endeavors that come off as purely nothing but popsci clickbait trivia of going against everyone's better intuition for nothing less than trying to make someone feel dumb for being smart. [math]0.\bar{9} = 1[/math] and Ramanujan's [math]-\frac{1}{12}[/math] arbitrate a sense of retardation over the masses in attempts of communicating the idea that obvious common sense is somehow mathematically, scientifically incorrect, and both these in particular rely on abusing infinity explicitly because it is vaguely defined to allow it, against your claim of its consistency or ability to prove truth.

Infinity is actually garbage and has no functional reason to exist in math, on top of being explicitly immoral in trying to defend it.

>>9737502
Being moralistic like this about math is kind of autistic man. There's a lot of math you can do without the axiom of infinity, but some useful math depends on it. Popsci is in every field, that doesn't invalidate the actual mathematics. Yes, infinity is often unintuitive, but nobody is hurt by their intuition being violated. The [math] -\frac{1}{12} [/math] stuff that ramanujan did is only remarkable in that his not quite justified manipulations gave him the same value as the analytic continuation of the riemann zeta function which assigns a number to that series. Sometimes in quantum mechanics you come across divergent series, and you can use analytic continuation to resolve these into finite numbers. So in a loose sense the [math] -\frac{1}{12} [/math] is used in applications. The zeta function is used in applied statistics often as well, even though for [math] s > 1 [/math] it is defined as [eqn] \zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s} [/eqn]
Anon, I want you to be honest with me, are you upset about all this because you failed Calculus? Many programming degrees require it and sometimes it causes people to drop out, so I have to wonder.

>>9737482
0*inf
undefined

>>9737502
>Infinity is actually garbage
It's a blunt tool,
but n/inf=0 is one result that applies

inf-inf
0*inf
inf/inf
are undefined

>>9737515
No I didn't fail a math course. Saying useful math depends on it is nothing but a claim. You're usually in the wrong of an argument if your first reaction isn't providing an explicit example supportive of your argument.

Can you give an example of infinity being utilized towards solving a real problem? There's been a lot of talk about engineers do this and that, but no real solid issue has been aroused. It's just been hypothetical engineers doing hypothetical work.

Happen to have a real example?

>>9737516
>>9737518
Those are indeterminate forms if you mean them as limits. Not necessarily undefined.
>>9737520
No, nobody has an example of an engineer counting to infinity. It is only used in an abstract sense like with convergent taylor series and infinite differentiation and such. The axiom of infinity does not say that a computer, person, or engineer can count to infinity. So if you will only accept someone explicitly achieving the infinite as an application then nobody will be able to give you an example of that, but that's not a very interesting observation. It's kind of a vacuous fact don't you think? If I give you an example of symbolic use of infinity you'll say that I'm moving the goal posts, so I'm not going to rehash that. You're right in that infinity doesn't exist in many sense, but stop saying it's inconsistent. There are no contradictions in how infinity is used, any contradictions you can pose involve implicit assumptions that automatically violate the framework infinity is used within, and as such are carefully avoided by mathematicians. Math is not concerned with reality or applications and as such it doesn't matter to mathematicians that people can use it or not. I've only been giving you real world examples to appease you, and you're just going to make your requirements tighter until it's vacuously impossible to prove you wrong. I don't actually care about applications so fuck off and talk about how dumb mathematicians are with your code monkey buddies and leave us alone. I think we would both be happier if you stopped making these threads.

>>9737520
All of analysis and calculus is developed using the notion of infinity. That means the development of analytical methods to solve problems all around the field of science. But to be more concrete, consider https://en.m.wikipedia.org/wiki/Finite_element_method it's a methods used for numerical approximations, which while at the end is used to compute finite values, the developement of the methods and the proof that those methods work rely not only on calculus but on calculus of variations which require the notion of calculus to be generalized in a non trivial way, which cannot be developes with a finitists approach.

>>9737533
He said wikipedia is a jewish shill site so I tried to avoid linking it, here's hoping he doesn't use that to "refute" you.

>>9737520
>No I didn't fail a math course.
And yet you can't deal with basic things like limits of series?

>Saying useful math depends on it is nothing but a claim.
A trivially easy to support one.

>You're usually in the wrong of an argument if your first reaction isn't providing an explicit example supportive of your argument.
It's usually pretty safe not to provide an example when they're this obvious. Nobody cites particular dates when they tell you the sky is blue on a clear day.

>Can you give an example of infinity being utilized towards solving a real problem?
Newtonian physics. Combinatorics. Algorithm performance and big-O notation. Statistics. Basically anything hat requires more math than adding up a grocery bill.

>>9737537
Well, any engineering course offers finite element methods as a course. Don't know wat search engine he considers reliable enough to see this.

>>9737537
>jewish shill site
lol, ravings of a feverish child, classic poltrash

>>9737538
He'll say that those methods aren't infinite because double floating points only go up to 2e308. Literally impossible to reason with.
Can't fail a course if you never take it in the first place, although a couple months ago he did say he had a math phd (until someone called him out on it of course).
>>9737542
Yep, I just wish he would stop posting these threads.

>>9737538
He wants you to actually work out a problem in front of him instead of talking about the fields that apply it, he needs a step-by-step like a child.
And when you give it he'll move the goalposts and we'll be back where we started.

>>9737542
Maybe he's mad since so many mathematicians are jews?

>>9736842
streams, lazy evaluation

>>9737538
Here's what happens if you provide a real example.
>>9736979

>>9736842
while (1 == 1) system.out.print("u r and idiot");

infinite enough for you?

>>9737569
kek

>>9736842
"loop until *something it will never reach*"

>>9737560
That wasn't a legitimate use of infinity in the mathematical sense. Its an invocation of the memory address which is a real finite number, and it honestly doesn't use it in an intelligible way, or uses it in about the only intelligible way it can be used as determining whether or not a value is infinity via a boolean check, which truly is the most simple of mathematical checks possible short of assigning a variable in a statement like x=1.

Theres not even a strong invocation of iterative work that something like atan2 might require. It's merely checking if the math it has accomplished resulted in an answer larger than 1.7×10^{308} which is otherwise uncomputable without creating your own string based calculator, and if it isn't then to proceed with evaluation, which is an ultimate given considering evaluation operators don't perform on the datatype max value of infinity. So even fucking still then, the only reference to infinity in the entire include is literally making sure the result is a real number and explicitly not greater than 1.7×10^{308}

I feel like you just typed infinity into google going through github and grabbed whatever the fuck popped up.

>>9737569
Not if i turn off my computer.

>>9737594
>invocation of a memory address
Check your memory address for when I said that computers don't matter to this conversation, and how they "reference infinity" is immaterial.

>>9737601
I was talking to >>9737594
Who provided >>9736979 as somehow indicative of being a truthful argument, which it wasn't.

>>9737611
Talking to >>9737560

>>9737611
Please just leave /sci/, we don't like you and you don't like us.

>>9737614
>bitching and complaining

>>9737616
Is all you've done since you started this thread.

>retard implying infinity is a number because IEEE 754
>butthurt mathematicians won't stop giving him (You)s
Stop it.

>>9737617
This is not my thread.

[math]\tiny \text{My thread already hit bump limit yesterday :^)}[/math]

>>9737594
Are you really trying to claim that the meaning of a program can't depend on our ideas about infinity, because the actual; implementation of the program will be performing computations on a finite set of numbers?
Because that's simultaneously the wrongest thing I've heard about programming and mathematics all day.

>>9735034
BAD post

Rewrite 0.999... to a geometric series and solve.

>>9737631
A similar program written in a different way might have had something like if (x < 100)

Replace 100 with """infinity""" aka 1.7× 10^{308}

i was just being truthful.

>>9737641
(0.5)(0.5)

>>9737644
>A similar program written in a different way might have had something like if (x < 100)
No it wouldn't, because then the program would be doing a different thing.

>Replace 100 with """infinity""" aka 1.7× 10^{308}
No.
The goal is the provide a model of the required behaviour at a sufficiently distant point. The theory that describes why that's meaningful depends on infinity.

>>9737681
When you're treating infinity as a real finite number, it doesn't matter what number you substitute retard.

>>9736842
Kruskal and prims. Both use infinity as placeholders

>>9737695
>When you're treating infinity as a real finite number, it doesn't matter what number you substitute retard.
It obviously does - that's what determines the quality of the results you get.

>>9737704
I think we should be clear that regardless of the method, 15 digits of accuracy is all you're resolving. That gets worse for extremely small or extremely big numbers. Like in the case of 1 ×10^{307}, the number is presentable between 1.00000000000000 × 10{307} and 100000000000000 × 10^{292}
unless a single increment modifying this value is equal to or greater than 0.00000000000001 × 10^{307} || 1 × 10^{292}, then an increment doesn't occur. The quality of accuracy of a number this large is 15 in 3 googols where you may as truly well just use a boolean check to see if the result is real or not, and if its real then you do something unrelated to the calculation. 15 parts in 3 googol is like correctly guessing the exact locations of every possible plank length of the earth given a 3 dimensional array of plank length cubes containing the entire volume of the universe. Getting infinity in computer math is usually not a feature, but instead an indicator of an accident.

>>9733681
Math is for computers. Let the computer fucking figure it out instead of sitting around playing with numbers all day like a fucking autistic loser.

>>9737961
>math = arithmetic

found the fatburger

>>9733681
Yes lim(x->1-)(x) so close to 1 it might as well be 1
The distance between those two numbers is infinitely small.

is 0.000...1 = 0?

>>9738017
No because it ends(since you added the 1 at the end)
But 0.00000.... is 0

>>9738025
so 0.999...9 and 0.999... are distinct numbers?

>>9738028
0.999...9 isn't well defined.

>>9738030
are you saying you could define 0.999...9 as 0.999...?

>>9737995
We can restrict attention to integer arithmetic, except that it makes things very cumbersome.

Surely OP would volunteer to write a code that takes a Diophantine equation as input and correctly either outputs a solution, or a proof that none exists. And also OP would provide bounds on the running time of this code.

>>9738017
yes

>>9738025
>infinity ends
k

>>9738028
no, both are 0.9...

>>9738069
When did i say infinity ends? I just said it is not an infinite row of numbers.
It clearly ends it has a 1 in the end.

>>9738108
so either the ellipse or the 1 is bullshit
fuck the 1

>>9738028
No, the first number has finite digits, the second doesn't.

>>9733681

Oh no, it's this thread again..
(--_--)"

How many of these threads do we have in 1 day? How many do we have in 0.999... days?

>>9737596
well then im afraid that's not part of turing's model of computation and that would be in your error as you would just be using computers wrongly at that point

>>9736704
sqrt(-1)?

>>9736070
>too much of a brainlet to see that theorems arising from geometric series are not [math] based [/math] on the [math] result [/math] that 0.999...=1

daily reminder that i, as a person, understand infinity
daily reminder that people are computers
daily modus ponens that computers can use infinity

>>9738324
You don't understand infinity. You think you do cause you're a hellbound brainlet suffering from pride.

Computers also don't use infinity. People were challenged to provide an example and no real example was provided.

You have sub-animal intelligence.

>>9734515
I hate this justification, it just presupposes decimal expansions make sense.

>>9738324
>computers can use infinity
not as a number they can't,
see wolfram for an example, uses infinity but sure as hell not as a 'uuuge numba

>>9738340
quit projecting caues you dont knwo how infinity works lol

>>9738346
bro, I"M a computer and i use infinity all the time. ergo, it's fine

>>9738344
It supposes 0.333... is exactly equal to 1/3, even though 0.333... is just an arbitrary amount of finite 3's and for any finite string of 3's, the value is less than 1/3.

1/3 > 0.3
1/3 > 0.33
1/3 > 0.333
1/3 > 0.3333
1/3 > 0.33333
1/3 > 0 333333
1/3 > 0.3333333
there never occurs a rightmost digit that isn't 3, and infinity has no finite end so there are always more finite digits ahead.

>>9738347
Shut up you fucking broken piece of garbage. Just do yourself a favor and save your fucking breath for when the water rises above your head.

>>9738350
See >>9736620

>>9738350
>let's pretend infinite is finite

>>9738351
chill bro, triggered much?

keep calm and infnity on lmaoooo

>>9738355
>i have no argument

>>9738353
Incorrect
learn to do math.

Sums say nothing but sum. It doesnt imply you're supposed to converge or diverge or solve or express the solution of the sum in an alternative way.

[math]\sum_{n=1}^{4} \frac{3}{10^n} = 0.3333 \\ \sum_{n=1}^{\infty} \frac{3}{10^n} = 0.\bar{3} \\ \frac{3}{10^n} \neq \frac{3}{9} \\ \frac{1}{3} > 0.\bar{3}[/math]

>>9738357
bro lol i save all my arguments with when i argue with infinity about how it does and doesnt work

>>9738354
Whos pretending.
You can't reach infinity, and if you so much as try, all you get is a real finite number.

Stupid fuck. Are you this stupid? Are you so fucking stupid? Whats wrong dumb fag, did daddy beat your booty too hard as a kid? Couldn't ever stop being a little prick nigger to everyone you ever met? Or maybe he couldn't cause he had ALS cause he was a sub-animal, and now he's passed his stained dead-end legacy onto you.

>>9738358
So you agree that sum from n=1 to inf of 3/10^k = 0.333...

By the convergence theorem, this is equal to 1/3.

Do you admit 1/3 = 0.333...

>>9738366
Learn what a Cauchy sequence is you troglodyte.

>>9738366
Wrong person. Sorry.

I meant to reply to this degenerate: >>9738362

>>9738366
Convergence = rounding = guesstimation
https://youtu.be/T7BlxTIH_bs

Here i just went and searched for a video more up your ally of mathematical proficiency you goddamned literal toddler.

upboat this post if you're a liberal who understands infinity

>>9738373
>Convergence = rounding
Wrong. The infinite sum is equivalent to the value it converges to, not an approximation of it. Limits have infinite precision.

>>9738385
>infinite precision
[math]\huge\text{D N E} \\ \huge\text{DOES NOT EXIST}[/math]

>>9738373
>rounding
So what is the rounding error between 1/3 and 0.333...?

>>9738389
Plus or minus an infinite amount of extra 3's.

>>9738388
deformed-feels-guy.png

>>9738391
angry-nintendo-switch-wojak.gif

>>9738362
My dad was black so he wasn't around.

>>9738388
Infinite precision doesn't exist for a measurement, but does for certain mathematical values. For example, 4 is the perfectly precise value of 2+2.

>>9738388
Of course it exists, otherwise the sum could not be said to converge at all. The sum converges because there is no error term that can separate the limit and the sum regardless of how many terms you sum. If there is no distance between two numbers they must be the same number.

>>9738390
An infinite amount of 3s describes many different numbers. You'll have to be more specific.

>>9738396
I believe the value you're referencing is [math]4.\bar{0}[/math], the most 4 a value of 4 can be. The alpha 4.

Imagine the alpha 4 having to put up with [math]3.\bar{9}[/math]

4 . 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...
3 . 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 ...

Alpha 4 has infinite precision of final equivalence in 0's but betacuck 3.999... doesn't even have one element of final precision let alone infinite. Poor little 3.999... retard thinks he's an alpha 4 thougg. Everyone can see his 3. Everyone can see his 9's. Hes no perfect 4 point OH much like your sub-animal GPA.

>>9738397
>infinite distance = no distance
We'll, you're not wrong. You're wrong in extrapolating any incremental behaviour though. 0.9999.... cant exust because if there were truly infinite expansions, it provides no logical incremental ability to reach 0.99 from 0.9

1/infty = 0
Move 0 decimal spaces forward

Guess there are finite 9's :^)

>>9738407
3.9999999
+.1
4.0999999

3.9999999
+.01
4.0099999

3.9999999
+.001
4.0009999

3.9999999
+.0001
4.0000999

3.9999999
+.00001
4.0000099

3.9999999
+.000001
4.0000009

3.9999999
+.0000001
4.0000000

3.9999999
+.0000000
4.0000000 !!!!!!

>I DELENEGATED DUH 1 TO INFINNINY SO I DONTS GOTS TO REACH IT AND UH 3(DOT)9 PLUS 0 IS EKWALS TO 4

>has to see a number expressed in writing to be sure of its existence
the absolute state of the computing humanities

>>9738390
Let E be the alleged error term.

Then 1/3 - sum from k=1 to n of 3/10^k >= E for all n

1/3 - (3/10)(1-1/10^n)/(1-1/10) >= E

n =< log(1/(3E))

So whatever you allege to be the error term cannot be, since there is a partial sum to some n > log(1/(3E)) which has a smaller error term.

This thread is why I have no respect for code monkeys.

Your ignorance is no argument. Learn some analysis and then come back.

>>9738437
Hey you aren't being very kind to infinity.

>>9738439
A math education without knowing how to program is like a chef without a kitchen.

You are worthless.

>>9738410
>You're wrong in extrapolating any incremental behaviour though.
What does that have to do with my proof? You've admitted every part of it is true now, so you lose.

>>9738442 did you get filtered out by algebra or by analysis?

>>9738445
Um, no sweetie. I marked you wrong on convergence and I marked you wrong on your interpretation of infinity. No one admitted anything to you.

>>9738448
I had ab education unlike you who missed K-12
https://youtu.be/T7BlxTIH_bs

>>9738441
So you admit there is no error term and that converged is not rounding.

>>9738442
LOL, you Orangutan.

I first began to program using Javascript at the age of 13 with Runescape private servers. Your career is my child's play.

A code monkey is to a computer scientist what a mechanic is to an engineer.

Your beliefs on finitism were resolved in the 1800s. Come back in 200 years when you're up to speed.

>>9733687
Engineer here. Literally never used that.

>>9738456
No, you're just pretending infinity is a finite number, which is wrong.

You get a finite number from approaching infinity, yes. This is fine.

Infinity itself is not a finite number though, and cannot be attained. Its wrong to treat infinity itself as the finite result just cause you're a brainlet who doesn't understand why he keeps getting finite results when aiming for infinity.

>>9738452
You have no argument against my proof, and you admitted each part. You lost.

>>9738464
>No, you're just pretending infinity is a finite number, which is wrong.
Where did I do that?

>Infinity itself is not a finite number though, and cannot be attained.
What does attained mean mathematically?

>>9738455
you're right. my pre-school teacher put in a good word and i skipped right to mit post-doc after kindergarten

>>9738465
You are a psychotic retard who makes up stories. No such admittance ever occurred. Quote the posts if they exist. They dont. You wont. Or maybe you'll just quote random posts and anyone who clicks through them will read them and be like "uhhh..? Didn't happen"

Then they'll realize you're that retard from yesterday who has his argument forfeit cause he was just stringing everyone along with any substantial info to back up his claims.

Waste someone else's time.

>>9738462
So you've never solved a differential equation? In order to solve one you must know that the solution is unique.

He did not state that engineers prove the Banach fixed point theorem; he stated that you assume the solution given initial conditions 1. exists. and 2. is unique. Your reading comprehension needs work. You and the code orangutan should repeat middle school and come back when you're ready to speak with the adults.

>>9738362
>reach infinity
inf isn't a real number, so?

in your retard world you can't reach 1 either

>dipshit crayon eating bus stop mastubator

>>9738469
More like you died in the womb and this entire world has just been a fleeting DMT fueled death fantasy as you're ushered to hell without a baptism.

>>9738478
>This troglodyte believes the myth that DMT is released upon our deaths as though natural selection gives two shits what we experience when we die.

>>9738471
Here >>9738358 you admit the infinite sum is equivalent to 0.333...

Here >>9738410 you admit the convergence theorem is true

>>9738481
Well, normal people will experience it. You might not given you're not suppressing anything. Your existisence is just an out-in-the-air wafting fart.

>>9738471
So what is the error term?

>>9736828
I came here with the sole purpose of laughing at you

>>9738484
Yes and no.
The "infinite" sum 3/10^n does indeed produce a never ending string of 3's. In the same post it says that 3/10^n is not 3/9 though. You also disregard the posts that provide for 1/3 being greater than any number between and inclusive of 0.3 - 0.333....


No to convergence because 0.999... would not exist under infinite expansion, as any one decimal element would be equal to 0. You would get 0.9 and never be able to attain 0.99, firstly, and secondly convergence is just brainlet rounding.

I dont think i've included any extra information that wasn't in the posts you quoted so you're just a shithead who can't read.

>>9738499
> In the same post it says that 3/10^n is not 3/9 though.
By the convergence theorem, the infinite sum is. You have still not disproved the convergence theorem.

>You also disregard the posts that provide for 1/3 being greater than any number between and inclusive of 0.3 - 0.333....
Which posts show than 1/3 > 0.333...? I have repeatedly asked you to provide their difference, and you have not given me a number.

>No to convergence because 0.999... would not exist under infinite expansion, as any one decimal element would be equal to 0.
Again, what does this have to do with convergence?

>You would get 0.9 and never be able to attain 0.99, firstly, and secondly convergence is just brainlet rounding.
Again, what does "attain" mean mathematically?

You have no argument and you admitted mine was correct, you lost.

>>9738510
Eh. No such admitting occurred. This was explained twice now so you've evidently lost so much that you're just skipping as a broken record.

>>9738543
I already showed you the posts where you did so. And once again you purposefully ignored my responses to your argument, because even you know you lost.

>>9738552
Like the broken record you are, you disregard proof and argument.

I do not doubt you're an atheist.

>>9738559

>>9738559
>disregard proof and argument
>meanwhile hasn't answered a single question or given a single counterproof

>>9735402
No no no.

The interval cannot be pi as pi isn't in the set.

>>9735402
This is actually interesting, because in this case you can't even express the number that is infinitely close to pi without referring to the hyperreals or something, maybe you could do 0,999...*pi, assuming we know how to multiply these things when we're throwing things out the window.

>>9738622
The number infinitely close to pi is pi.

https://en.wikipedia.org/wiki/Completeness_of_the_real_numbers

>>9737520
Your problem, you absolute sniveling retard, is claiming that math must be "useful" in to be real the first fucking place.
Mathematics is the objective underlying reality REGARDLESS of whether or not 115 IQ engineer faggots use it to build shitty products that break down in 10 years, you fucking scum sucking retard.
Infinity exists intuitively, I can ALWAYS add 1 to anything, forever. A fucking child can grasp this concept you computer shiticist. Uncountably infinite sets are easy to understand by just studying elementary sets.
Kill yourself.

>>9738034
Underrated reference.

bad thread
sage

>>9738631
3.14159 = pi

its really important to understand the concept of decimal accuracy which doesn't seem to be a validated idea in math. Decimal accuracy is what determines how much work is done. Do we need an answer with 4 decimal places, or 20?
Do you believe there is any coherent implement of pi up to even just a million decimal places? Of course there isn't.

This of course ties in with the idea of infinite arbitrary decimal accuracy: It doesn't exist. You're not going to functionally use something like "0.333..." to any greater accuracy than you'd use for a transcendental irrational. If you're calculating with pi at 3.14159, then you're calculating [math]0.\bar{3}[/math] at 0.33333

infinite arbitrary accuracy is fiction, like orcs and elves in the Lord of the Rings. Math is supposed to produce real hard results, it's not a goddamn liberal art.

>>9738636
You're misinterpreting infinity and overestimating your ability. You can't increment over 1 forever. You will die one day. And your misinterpretation stems from the belief that you can't increment at all unless you can increment without bounds, which is retarded. You can increment to 10 under a maximum boundary of 10. You can increment past 10 because the decimal system functions as such. Neither of these truthes require infinity to exist.

Even still, no matter how you increment you never reach infinity regardless if you believe it exists or not. You and I could both increment unendingly, and even though i know infinity doesn't exist and even though you think it does, neither of us will ever increment to infinity. If that isn't enough of an impartial unbiased fact, then i dunno what to tell you.

>>9738835
what if i start at infinity minus 1 then increment once.. then i'm at infinity

dipshit

>>9738849
>imfigany minum one

>>9738811
Decimal accuracy is usually left alone because most math remains true regardless of it.

For example, an equation will be written 3pi and not 3× 3.1415

This of course changes in retardulus wit iterative sum and mult structure. The quality of your equation is not based in constants like Pi, but instead upon the number of iterations. [math]\sum_{n=1}^{6} \frac{9}{10^n} = 0.999999 [/math] is a number creation format that the rest of math doesn't use.
Now, the rest of math already knows to not use infinite decimals of accuracy, and because of the value of the constants allows for any real finite sought accuracy without changing the equation. In calculus though, there is a hardcoded element of accuracy implied by the iteration limit, which is abused to no fucking end when people set n=1 to infinity but only use 7 digits of accuracy in their answer. Beyond the simple fucking braindead niggery that these people assume happens at n=infinity, or that it even can happen, they're undercutting it all by doing completely unecessary work. If they need 7 digits of accuracy, then their work shouldn't be [math]\sum_{n=1}_{\infty}[/math] but rather it should be [math]\sum_{n=1}^{7}[/math]. And if you're trying to create a transcendental number from iterative work like this which might take a hundred steps just to accurately get 10 decimals, then whatever, increase your work limit, or rather set it as a solveable variable to determine how many steps are required to get x amount of decimals accurate.

>>9738811
>3.14159 = pi
Wrong.

>its really important to understand the concept of decimal accuracy which doesn't seem to be a validated idea in math.
Is really important to understand the definition of pi if you are going talk about it.

>This of course ties in with the idea of infinite arbitrary decimal accuracy: It doesn't exist.
In math it does.

>You're not going to functionally use something like "0.333..." to any greater accuracy than you'd use for a transcendental irrational.
All of mathematics functionally uses all values with infinite precision. Try again.

>>9738971
See >>9738895

>>9738974
None of that responds to anything I said. There is no "abuse" in calculus. The infinite sum is well defined and consistent. Just because you don't understand high school level calculus doesn't mean it's wrong, brainlet.

What's wrong with this proof?
Let x = .999...
10x = 9.999...
10x - x = 9.999... - .999... = 9
9x = 9
x = 1
.999 = 1

>>9739115
If
>.999 = 1
Then
>9.999... - .999... = 8.999...
What you're doing is like trying to simplify pi by taking it and subtracting (pi - 3).

>>9738442
Tell that to Euler you compiler cuck.

>>9736828
I came from /g/ just to laugh at your brainletism

so there's no number before 1.0?

also, i saw a guy explaining this on YT saying 0,9... is an infinite number, so removing parts of it wouldn't make it less infinite... sure, but it wouldn't be the same number, right? if you remove the second nine from it, for example, it would be 0,909... instead of 0,9..., right?

i'm a math brainlet btw, don't wanna spread misconceptions

>>9737569
roasted and toasted

>>9739425
There's no real number immediately preceding any other real number, yes.

>also, i saw a guy explaining this on YT saying 0,9... is an infinite number, so removing parts of it wouldn't make it less infinite
Wrong, subtracting any nonzero amount will change it. There is no such term that applies to 0.999...

>>9739516
thanks, might just read the whole thread then, since the guy's explanation was entirely based around that

>>9739516
>0.999... = 1 because i'm literally a fucking inbred retard mongoloid
0.99999...99... = 1
0.89999...99... = 0.9
0.98999...99... = 0.99
0.99899...99... = 0.999
0.99989...99... = 0.9999
0.99998...99... = 0.99999
0.99999...89... = 0.999...

tire fire is your new home now. Garbage truck is now your wife.

>>9739542
>0.98999... = 0.99
Hm...

0.21999... = 0.22
0.22219... = 0.2222
0.222...1999... = 0.222...

[ ... 2 2 2 1 9 9 9 9 9 9 9 9 9 ... ] =
[ ... 2 2 2 2 2 2 2 2 2 2 2 2 2 ... ]

>>9733681
This expression is impossible to write in base 2 and still be convincing.

>>9739115
Infinity is treated as a dynamic variable in that problem
>x = 0.999...
>10x = 9.999...
it literally just changed the value of x.

use smaller numbers
>x = 0.99
>10x = 9.9
in normal arithmetic, multiplying by 10 just shifts the decimal place over. If we have two 9 elements in 0.99, we still have two 9 elements in 9.9

the infinity way is invalid cause when x=0.999..., x has infinity 9's elements, but 10x=9.999... suddenly has infinity plus one 9 elements. Its not actually valid, real math. If this method is suppose to be acceptable, then it should be acceptable to say
x = 0.99
10x = 9.99

it isn't though. It's just incorrect math.

>>9739868
x = 0.9
10x = 9.9
10x-x= 9.9 - 0.9
9x = 9
x = 1

0.9 = 1

>>9735521
>if 0.999... = 1, then what about a number infinitely close to 0.999... like 0.999 but with an 8 at the end.
If it has a 8 at the end, name it's position.
>anon it's position X
I append 5 to your number and I have a number closer to 0.(9).
>anon it's at infinite position
contradicts positional exponential system

>>9736627
>Its not an amount or a size.
Infinite sums theory you piece of shit.

>>9739868
>it literally just changed the value of x.
wow is this /b/

Kek at the absolute fucking brainlets who think infinity is a useless concept just because they can’t count to it on their fingers. Imagine being that retarded and incapable of abstract thought. Jesus Christ.

>>9739542
0.99999...99... = 1
0.89999...99... = 0.9
0.98999...99... = 0.99
0.99899...99... = 0.999
0.99989...99... = 0.9999
0.99998...99... = 0.99998... FTFY
0.99999...89... = 0.999...

>>9740179
If you think about orcs and elves abstractly, will this endeavor help you in any way whatsoever.

you are a not thinking in abstract ways. You are thinking in imaginary and delusional ways.

>>9736828
>what is a loop.

>1+2+3+...=-1/12

>>9740392
ubboat

>>9733718
how about 1.00000000000000000000....

/g/ here, thank you for bringing this garbage there too, /v/ crossposting retards weren't enough.

>>9740651
sad thing is, by moving the garbage there, the quality of both boards went up

>>9733681
It's pretty basic limit theory

>>9736828
/g/ anon here
Infinity in programming is logically dealt with in the same way you deal with regular math. You never actually calculate 1+ infinity, but when your functions interact with infinity, you deal with it.
An example would be visualization of the Mandelbrot set, you can render it at infinite resolution, with infinite iterations per pixel, but you limit it's iterations and resolution according to need.
Programmers are aware that infinity isn't a number, but I'm not sure if you do

>>9736842
While (true)