Why do people struggle so much with the idea that .999...=1?

[Anonymous No.11612986]

Is it a mental limitation? Not being able to conceive of infinity? It's been settled math for over a century now.
I remember a conversation I had with my daughter in the car when she was starting out with algebra...
>Me: Is 9.999... the same as 10, or is it just really close to 10?
>Kid: Really close. It never gets all the way there.
>Me: Well then how close? What do you get when you subtract 9.999... from 10?
>Kid: (pause) An infinite number of zeroes. . .and then a one. . .wait, you can't do that.
>Me: Right. You just have an infinite number of zeroes. Which is zero.
>Kid: (pause) Oh, that's mind-blowing.
Even a child can come to acknowledge the infinite, it's all quite trivial really, but apparently still too much for lesser minds. *sigh*

[Anonymous No.11613031]

>>11612986
If you can't algebraically represent a number then what's the point of having a way to express this concept? in other words: 0.999... is meaningless.
If you want to explain what a limit is, then explain what a limit is, don't create some magical lexical device to impress some dull kids.

[Anonymous No.11613042]

>>11612986
LISTEN TO ME YOU FUCKING ATHEIST FUCK, STOP MAKING THIS SHIT THREAD ALREADY. 1 = 0.99999... . NOW PLEASE LEAVE.

[Anonymous No.11613074]

Infinity is not real

[Anonymous No.11613084]

>>11612986
>settled
Whenever someone says terms like "settled science" you know they're spewing bullshit.

[Anonymous No.11613086]

Infinity doesn't make sense if you try to analyze or justify it beyond the gradeschool assumption that "it is the biggest number"; so your story is retarded fake and gay bullshit OP.

0.999... isn't 1 no matter the circumstance. "Close enough" is a measure of finiteness.

[Anonymous No.11613087]

>>11612986
Less than 1 is not the same as 1.

[Anonymous No.11613109]

>>11612986
It is indeed a mental limitation and it's in the heads of those who believe "0.999..." is the same as 1. The core of the mental problem in their minds is as follows:

Their inability to comprehend that ".999..." isn't the same as "1" is directly tied to their inability to grasp eternity and infinity. Their minds have basically been programmed to believe eternity and infinity are impossibilities. Over the course of many generations of indoctrination into an alien worldview, their parents and their parents etc gradually "learned" to be unable to comprehend it and this "learned disability" was inherited, and encouraged/fueled by various external factors from the echoing modern culture.

So basically, they're mentally damaged.

This difficulty they have with eternity/infinity shows up in many different fields, from math to astrophysics.

This mental handicap is inherited directly from the (((Abrahamic))) religions, more specifically (((Christianity))) for us Westernerns. In it's origin, the inability to understand infinity and eternity is 100% Judaic in thought/philosophy. In contrast, the non-Jewish man; the Pagan man, at least the /European/ Pagan man, never had any problem with infinity and eternity. (((Christianity))) introduced into the minds of people the idea of life and the world/universe being linear, starting from point A and ending at a point B, whereas in the Native European worldview everything is an infinite circle.

That's why many people today can't understand that .999 repeating forever will never reach 1 - they refuse to accept the idea of an infinite/eternal repetition. Saying "it's 1" is their method of escaping from the uncomfortable (and to them insurmountable) challenge which the concept of infinity/eternity is to their Judaically-induced mental disease.

[Anonymous No.11613116]

>>11613109
Very related. A slip-up from one of the "less than 1 is the same as 1" promoters, showing he can't mentally accept that infinity/eternity is real.

[Anonymous No.11613125]

>>11612986
>Why do people struggle so much with the idea that .999...=1?
because people don't understand that strings of digits are not literal numbers, they're just notation which we use. they think that 0.999... = 1 means "two distinct numbers are actually equal" which is obviously paradoxical.

[Anonymous No.11613157]

Stop shitposting

[Anonymous No.11613186]

>>11612986
See: >>11613157

[Anonymous No.11613207]

>>11613125
Repeating digits are indeed not real numbers in decimal. They often exist perfectly fine in fractions or otherwise rendered as an identity outside of decimal. For example [math]\pi[/math] doesn't actually proveably exist. There are plenty of indications to assume it exists, but the unlimited degree of accuracy required to accommodate that pi symbol in Decimal are distinctly greater than the finite degree of accuracy acquireable. You only need about 10 digits of pi to accurately accommodate virtually any measurement involving pi, but pi isn't actually 10 digits; nor is it actually 50 trillion digits. It likely has more digits than can possibly be discovered in either sense of having a Large Number amount of decimal places or an "infinite" unlimited amount.

Extend this process to whether "1÷3 = 0.333..." is actually a true or false statement. It obviously requires it to be false; the Fractional identity [math]\frac{1}{3}[/math] is clearly greater than any string of Decimal 3's in "0.333..."
The issue is that this problem has long been passed, ignored, taken for granted, and incorrectly asserted into education, and we find ourself in a world of hard decimal cutoffs integrated into calculators and computers. Not only are aspects of infinity relative to numbers ignored (as it should be), most calculations don't make it past 15 digits for virtually anything. Not just obviously finite, but finite to a degree that even children can easily comprehend.

Calculators and computers merely carry one more digit than necessary and use it to round a final answer. Explicitly rounding with explicitly finite digits easily accommodates "0.999... = 1"; and literally nothing less than explicitly rounding with explicitly finite digits.

[Anonymous No.11613218]

>>11612986
Because 0.999... is not 1

[Anonymous No.11613219]

I'm so glad you retards made ANOTHER thread about this to samefag to bump limit.

[Anonymous No.11613268]

>>11613219
It's not unlikely that an apocalyptical event occurs that could have been avoided had greater decimal accuracy been accommodated; which wasn't available because history ignored the task of reforming maths and insisted it was fine enough to just cutoff decimals and round after spending half a fucking breath to write out or compute a mere handful of digits.

[Anonymous No.11613275]

if 0.999 is equal to 1, then, in R, are open intervals topologically the same as closed intervals?

[Anonymous No.11613293]

>>11613275
0.999... doesn't exist inside R unless 0.999... strictly has some finite amount of decimals.

Cantor was a brainlet btw.

[Anonymous No.11613304]

>>11613293
I'm not a mathematician, but isn't 0.999... a real number? Why? Actually, if 0.999.. =1 then it surely belongs to R.

[Anonymous No.11613316]

>>11612986
Why is /sci/ so much more shit than HN?

https://news.ycombinator.com/item?id=23004086

But GJ for spamming this so hard for so long that it's gained traction, I guess.

[Anonymous No.11613329]

Not a single person in this thread exhibited a coherent idea surrounding this topic. Go learn basic real analysis.

[Anonymous No.11613335]

A lot of people just struggle with the notion that any given number can be expressed in different ways that are completely equivalent.

[Anonymous No.11613337]

Because they're think of it as a process rather than a value.

[Anonymous No.11613342]

>>11613329

can you please answer my genuine questions, then? not trying to bait: >>11613275
>>11613304

[Anonymous No.11613344]

>>11613275
Explain how that would follow (it doesn't). I'm just curious to see what you're reasoning is.

[Anonymous No.11613357]

>>11613329
>noooo people don't respond to troll threads seriously!!!!

[Anonymous No.11613374]

>>11613344
Well, I never studied topology beyond glancing at wikipedia for definitions of stuff that was mentioned when I was studying other subjects, so it's expected that I might be saying something stupid.

For me 0.999... is the perfect analogue of the left border of an open interval like [math] ]1,x], x\in R and x>1[\math]

[Anonymous No.11613377]

>>11613374
btw, fuck javascript

[Anonymous No.11613384]

>>11613342
0.999.. is a real number yes, because the real numbers are closed and contain all of its limit points: 0.999... is by definition the limit of a sequence of partial sums (it is in particular a geometric series).

I dont know how to answer your question about open and closed sets. If there existed a homomorphism between a closed set and an open set, both sets would be forced to be open and closed because open maps take closed sets to closed sets and open sets to open sets. Since R is connected, there are no proper open and closed sets.

[Anonymous No.11613400]

>>11613374
I don't understand. What do you mean by analogue of the left border? Are you suggesting [0.999... x] = (1,x]? If that were true, then every open set is also closed, making the default toplogy on R totally disconnected. Actually, I'm glad you raised this point. You can draw the above absurdity if 1 isn't 0.999...

[Anonymous No.11613403]

>>11613384
I understand your reasoning on the mapping from open set to closed set cannot be possible with a homomorphism, and it makes sense to me.
However, what was meant by this, then >>11613293 just bait and/or ignorance?

>Since R is connected, there are no proper open and closed sets.
Isn't the notion of open set a generalization of an open interval in R? Or does the word proper have some significance here?

Also, it's seems really weird to me that everyone in mathematics knows about this curiosity of 0.999...=1 but hasn't thought about it in terms of topological boundaries.

[Anonymous No.11613417]

>>11613304
Difference between "the set of real numbers" and what a real number actually is.

"The set of real numbers R" is a dumb niggerbrained meaningless concept made up by cantor but his shitty dumbass definitions and axioms basically require that every element in an infinite set must be, itself, finite; else infinity itself is an element contained within the set and presumes infinity is a literal real number.

0.999... isn't a real number in the sense that it actually contains an infinite expansion of 9's unless infinity is strictly a real finite number itself; or rather that "0.999..." only contains a finite expansion.
In the technical sense of accommodating infinity, "0.999..." is not even a real actual number, so whatever it's supposed to be may as well just be 1.

If 1-to-infinity were scaled down between 0-to-1, 0.999... is equivalent to "infinity minus 1", which is indeterminable nonsense because infinity isn't supposed to actually be a number. But infinity itself is also indeterminable nonsense as a number, and so "(infinity - 1) = infinity" is analagous to "(0.999...) = 1"

"0.999..." doesn't exist in R if the assumption is "0.999..." contains an infinite expansion of 9's. Any other finite expansion of 9's could exist in R though.

Its all busybody nonsense. In one case, 0.999... doesn't actually "equal" 1 because 0.999... doesn't actually exist.
In many other cases, 0.999... equals 1 because "0.999..." somehow implicitly assumes a finite degree of accuracy and rounding.

The problem with 0.999... not being a real number is one that stems from more basic and easily understood concepts. For example: Nothing lasts forever in this universe.
No real number contains an infinite expansion of decimals because nothing real lasts forever here.

[Anonymous No.11613418]

>>11613400
Yes, that is precisely what I mean, and what >>11613384 already answered in the same way you did. Thank you both.
It makes sense to me now. It's actually a neat way to prove this by absurdity, I guess.

I write ] instead of ( because I learned with the French notation.

[Anonymous No.11613427]

>>11613417
I don't see why a number that has infinite digits cannot be rational.

[Anonymous No.11613428]

>>11613329
>Go learn basic real analysis.
Go learn basic witchcraft, then you'll see that my crystals have healing powers.
>>11613316
>https://news.ycombinator.com/item?id=23004086
>all those idiot techies using the shit-tier algebraic "proof" and being smug about it
They really need to stick to writing webshit Javascript

[Anonymous No.11613435]

>>11613403
Proper just means it's not all of R or empry. R and the empty set aren open and closed sets (by definition), so saying there are no proper open and closed sets is the same thing as saying the empty set and R are the only open and closed sets.

I dont think mathematicians like to waste their time arguing about this. It is just such an obvious thing to anyone who has studied analysis. The only reason I'm still here is to answer your questions, and you're not being aggressive.

I'm not sure if that's bait or ignorance, but the statement itself is wrong. So yes, it's one of those things.

[Anonymous No.11613438]

>>11613427
Infinity as a concept related to numbers is irrational.

[Anonymous No.11613448]

>>11613438
As clever as that pun may be, you've just given yourself away. I do give you brownie points for that

[Anonymous No.11613464]

By the way, just to be pedantic, I guess what I actually meant when I was initially talking about the open interval was defining a number such that
x = 1.000000000...1
and then for all other y>x in R if it was the case that
[x, y] = ]1, 0], so I was actually approaching this from the wrong side, I should have thought this from the right side of the interval, so that for example
[0, 1[ = [0, 0.999...]
but I understood your points, anons

[Anonymous No.11613478]

>>11613435
Ok, thanks. It's not something I would spend a lot of time on, it's just that I was curious because it popped to my head and I took the chance that people that had studied this might be able to clarify it simply for me.

[Anonymous No.11613488]

>>11613435
and also, that makes sense because you can define a homomorphism to the null set or to R itself, so I understand the need for saying that

[Anonymous No.11613504]

>>11613448
It really is truly as simple as that though.
Infinity has never once been clearly defined to properly work within mathematics in a consistent way. It started strictly as a philosophical concept related to ponderings about the magnitude and scope of God by latin romans over a millenia ago. Had nothing to do with numbers or math til recent history. Cantor failed to properly define it even with his Axiom of Infinity, and postmodern usage of it in the age of computers just makes it the biggest number that can be addressed in a datatype, aka a big specifically finite number; "the biggest number". There are many different and contradicting interpretations of infinity in math.
All of them at least share how unnecessary and trivially pointless it is.
Like trying to describe God with numbers.
Trying to describe something that doesn't exist through a medium that doesn't acknowledge it in the first place.

[Anonymous No.11613537]

"Infinity" being hijacked to describe the unlimited nature of countable numbers is basically the same as fags hijacking the rainbow to mean gay sex.

[Anonymous No.11613619]

>>11612986
>hy do people struggle so much with the idea that .999...=1?
because they haven't taken basic real analysis where they construct the reals.

[Anonymous No.11613632]

>>11613031
>If you can't algebraically represent a number then what's the point of having a way to express this concept? in other words: 0.999... is meaningless.
[math] 0.999... = \limsup_{n \to \infty} {0.9, 0.99, \dots, a_n} [/math], where [math] a_n = \sum_{k = 1}^n \left( 9 \cdot 10^{-k} \right) [/math].
>>Kid: (pause) Oh, that's mind-blowing.
>with my daughter in the car when she was starting out with algebra...
things that never happened. there are better ways to make a point, undergrad.

[Anonymous No.11613638]

>>11613031
*
[math] 0.999... = \limsup_{n \to \infty} \{0.9, 0.99, \dots, a_n \} [/math]
where
[math] a_n = \sum_{k = 1}^n \left( 9 \cdot 10^{-k} \right)[/math]

[Anonymous No.11613641]

>>11613031
>If you can't algebraically represent a number then what's the point of having a way to express this concept? in other words: 0.999... is meaningless.
[math]0.999... = \limsup_{n \to \infty} \{ 0.9, 0.99, \dots, a_n \}[/math]
where
[math]a_n = \sum_{k = 1}^n \left( 9 \cdot 10^{-k} \right)[/math]
>>Kid: (pause) Oh, that's mind-blowing.
>with my daughter in the car when she was starting out with algebra...
things that never happened. there are better ways to make a point, undergrad.

[Anonymous No.11613669]

>>11612986
>Why do people struggle so much with the idea that .999...=1?
because I can imagine them as being distinct. Can you?
>reality > imagination hurr durr durr
This btw does not answer my question.

[Anonymous No.11613676]

>>11613669
If they're distinct, then there exists a nonzero difference between them. What would that nonzero difference be?

[Anonymous No.11613684]

>>11613676
>What would that nonzero difference be?
some kind of infinitesimal, obviously, as far as I know that doesn't have a representation in math, because infinity is as nonsensical as 0.00...001.

[Anonymous No.11613707]

>>11613676
0.9 + 0.1
0.99 + 0.01
0.999 + 0.001
0.9999 + 0.0001
0.99999 + 0.00001
0.999999 + 0.000001

How does this pattern continue?
Theres always a smallest rational part wherever you stop.
>b-but you don't stop
So you only ever count finite steps forever, no matter what.
>b-but infinity isn't finite
So you completed infinite steps, thereby making it finite...?

It seems that "how big is too big" and "how small is too small" are rational questions derived from the actually real limitations of the universe.

How small is too small that a decimal 0.0[...]1 number is too bothersome to deal with?

How many digits is too many digits that a 0.9[...]9 number is too long to deal with?

[Anonymous No.11613746]

>>11613684
>infinity is as nonsensical as 0.00...001
If there is no context, then everything is nonsensical. If you mean [math]\infty,[/math] then this is just the same of some otherwise very ordinary object that plays a special role when you talk about a theory. The notation 0.00...001 however has no meaning in mathematics whatsoever.

[Anonymous No.11613748]

>nothing comes after infinity
Technically nothing precedes it either.
More technically, infinity never comes at all in the first place.
More more technically is everything and anything can come after infinity because infinity isn't a finite end.
Cantor-technically, anything finite can come after infinity because infinity is an arbitrary indetermined finite natural number.
Double Cantor-technically is that infinity is TREE(3), the biggest finite number, of which no number can be greater, and the very definite hard limit cutoff end of numbers.

Nothing wrong or invalid about "0.000...1"

[Anonymous No.11613751]

>>11613746
>the same of
the same as

[Anonymous No.11613760]

>>11613748
>Nothing wrong or invalid about "0.000...1"
Tell us what it is supposed to mean then?

[Anonymous No.11613796]

>>11613760
I understand you read my post in reverse and started from the last line but please, continue reverse reading the post back up to the first line before asking dumb questions.

[Anonymous No.11613815]

>>11613748
Thank you for inserting a solid dose of gibberish into the thread. Not that it wasn't full of it already.

[Anonymous No.11613820]

>>11613796
So you just don't know?

[Anonymous No.11613833]

>>11613760
>Tell us what it is supposed to mean then?
Clearly, we take [math]...[/math] to signify [math]a lotta numbers[/math]. Hence, it follows directly that:
[eqn]...1 = a lotta numbers w/ one at teh end[/eqn]

[Anonymous No.11613834]

>>11613820
your inability to read is not indicative of my lack of knowledge. please don't reply at all if you only know how to project.

[Anonymous No.11613885]

>>11613834
I just assumed that if you know the answer, then you will present it. Since you refuse, then so be it.

[Anonymous No.11613891]

>>11613833
Is gibberish your first language, or did you adopt it specifically to use on 4chan?

[Anonymous No.11613908]

>>11612986
Here I can make some bullshit up too

Here's a conversation I had with a first grader:
>Me: Is 9.999... the same as 10, or is it just really close to 10?
>Kid: Really close. It never gets all the way there.
>Me: Well then how close? What do you get when you subtract 9.999... from 10?
>Kid: (pause) An infinite number of zeroes. . .and then a one.
>Me: Right.
>Kid: (pause) Oh, that's mind-blowing.

[Anonymous No.11613944]

>>11613885
The post you initially quoted where you asked for an explanation had 5 fucking justifications in it you brainlet.

The weirdest part is that you quoted the end of the post which necessarily required you read the rest of the post before it. There's no honest or good reason you should have asked the question you did. You're as dumb as language comprehension AI.
>the sky is blue
>"is the sky blue?"
>yes
>"wow avoiding, you don't know?"
>the sky is blue

Already asked you to avoid replying if all you understand is projection; which I'm gonna spell it out for you, is indeed the case. All you know is projecting.

Shut the fuck up and stop replying you dumb retard.

[Anonymous No.11613945]

>>11613908
That kid sounds clever. He explains what he means. In contrast that other anon refuses to explain his retarded and meaningless 0.000...01 stuff.

[Anonymous No.11613946]

>>11613684
>some kind of infinitesimal, obviously, as far as I know that doesn't have a representation in math
Yes, there are infinitesimals. Fortunately the only infinitesimal in the real numbers is 0 by design - that is equivalent to the Archimedean property.
>because infinity is as nonsensical as 0.00...001.
not really. See I knew this would come up. There is no infinite zeroes that lead to end with 1, since we could just as easily 'repeat' the countably infinite amount of leading zeroes and keep on going, and so on and so forth. hence there's actually no single instance of a 1 showing up here. again, this is due to the Archimedean property
>>11613707
Read the above. We don't do this proof via computation on a computer - the proof and its computational realizability are two different matters entire. read more recursion theory and computable analysis until you try and throw these arguments
>how big is too big
>how many digits
the answer is infinitely many lol

[Anonymous No.11613954]

0.999... is not equal to 1, but it is approaching 1.

[Anonymous No.11613955]

>>11613946
No the answer is like 16 digits.
16 digits is too many digits.
Don't be a dumbass trying to be a smartass.

[Anonymous No.11613963]

>>11613293
>1 doesn't exist inside R
wew lad

[Anonymous No.11613965]

>>11613955
>16 digits
stop being a dumbass pretending they're anything more than a dumbass. Anyone who has studied basic real analysis knows that 0.999... always provokes discussion of limits because its definition is inherently built on the supremum and limit definitions the reals were made to handle

[Anonymous No.11613966]

>>11613944
>5 fucking justifications
You mean the meaningless word salad? Not that there is anything wrong with that when you post on 4chan.
How about you continue to post the equivalent of grunting caveman sounds, and you leave it to me to explain mathematics? It seems a fair division of efforts into the thread.

[Anonymous No.11613971]

>>11613748
0.1=10^-1
0.01=10^-2
0.001=10^-3
:
0.0...1=10^-inf=0

[Anonymous No.11613973]

>>11613963
You might just be too dumb to breathe.

[Anonymous No.11613977]

>>11613954
>is approaching
0.999... is static, the length is aleph_0 from the get go.
Your naive cartoon vision of a diesel engine chugging along is ridiculous. Embarrassing even.

[Anonymous No.11613980]

>>11613973
sigh

[Anonymous No.11613986]

>>11613966
Pro-tip: Insulting easy to read sentences is just insulting your own intelligence. You're the only one here braindamaged enough to produce word salad.

[Anonymous No.11613993]

>>11613971
Of all the definitions for infinity as a number, not a single damn one of them allows for [math]\frac{1}{10^{\infty}}[/math] to equal zero.
You doubleshitposted just now.

[Anonymous No.11613995]

>>11613977
0.999... isn't static because it continues endlessly.

0.999 -> 0.9999 -> 0.99999 etc

[Anonymous No.11614002]

>>11613087
It isn't less than one, it's an alternative way to write one. You may as well argue 7/7>1 because "mOrE tHaN oNe Is NoT eQuAl To OnE".

[Anonymous No.11614007]

>>11613428
>I don't understand it therefore it's witchcraft!
Fuck off and learn something.

[Anonymous No.11614009]

>>11613993
1+2+3+4+... = inf
n/inf = 0
n*inf = inf
n+inf = inf
n-inf = -inf
0.999... = 1
https://www.wolframalpha.com/input/?i=1%2B2%2B3%2B4%2B......
https://www.wolframalpha.com/input/?i=10%2Finf
https://www.wolframalpha.com/input/?i=10*inf
https://www.wolframalpha.com/input/?i=10%2Binf
https://www.wolframalpha.com/input/?i=10-inf
https://www.wolframalpha.com/input/?i=0.999......

[Anonymous No.11614012]

>>11613977
>aleph
>sizes of infinity
>cantor brainletism
i'm afraid your disability is terminal, anon.
Your mom pooped you out of her vagina before you were done.

Go back and finish developing.

[Anonymous No.11614014]

>>11613995
>it has legs and runs around
kek

[Anonymous No.11614018]

>>11613995
What do you call numbers that are not static? Just non-static, or something more fancy, like "dynamic"?
Is 0 = 0.000... then static or not?

[Anonymous No.11614021]

>>11613669
I can imagine a continent between South America and Africa, so what? Why are you stupid enough to believe that your ability to imagine something has anything to do with anything?

[Anonymous No.11614022]

>>11614012
Impressive, did you quote that from your PhD?

[Anonymous No.11614026]

>>11614009
https://www.wolframalpha.com/input/?i=infinity
>>Infinity is an unbounded quantity greater than every real (and every whole) number.
https://www.wolframalpha.com/input/?i=quantity
>>a Quantity is how much there is or how many there are of something that you can quantify
https://www.wolframalpha.com/input/?i=quantify
>>to Quantify is to express as a number or measure or quantity
https://www.wolframalpha.com/input/?i=is+infinity+a+number%3F
>is infinity a number?
>>∞ is not a number
https://www.wolframalpha.com/input/?i=Does+1%2F%28not+a+number%29+%3D+1%2Finfinity%3F
>is "1/(not a number) = 1/∞" true?
>>no

Infinity is a concept made up by retards, for retards.

[Anonymous No.11614036]

Okay okay everybody shut up I have a proposal
>0.99... = 1 is partially correct because they represent the same value on a number line
>0.99... =/= 1 is partially correct because they are different types of numbers (one is real and the other is not)
So everybody is kind of right and the dispute is about what equality even means

[Anonymous No.11614037]

>>11614026
>unbounded quantity
you keep ignoring the first word
you keep ignoring the results

[Anonymous No.11614042]

>>11614026
Your shitpost is a ramble made up by a retard, for retards.

[Anonymous No.11614046]

>>11614036
>one is real and the other is not)
stop pissing in your cereal

[Anonymous No.11614054]

>>11614036
Wrong, stop using the Golden Mean Fallacy. The people who think 1=/=0.9... are WRONG, end of story.

[Anonymous No.11614055]

>>11613993
>infinity as a number,
lol, you're an idiot

[Anonymous No.11614074]

>>11614054
Anon I agreed that they represent the same value. I'm simply asking if part of the issue is that 0.99... is not an actual number and is just a funky way of writing 1, making an equals sign a bit misleading.

[Anonymous No.11614079]

>>11614074
0.90... is not an actual number and is just a funky way of writing 9/10, making an equals sign a bit misleading.

[Anonymous No.11614080]

>>11614018
0 = 0.0 = 0.00 etc
No matter how many 0s you add to it, it's going to equal the same.

9 < 9.9 < 9.99 < 9.999 etc
As you add 9s, it gets larger

[Anonymous No.11614085]

>>11614080
>As you add
how about when you die, does math change anon? or does it grow a mustache and legs and dancesdancesdances off to the sunset
>>11613977

[Anonymous No.11614106]

>>11614026
We can pick this apart for fun. Wolfram does not have the best writers for their documentation pages, that is already clear.

We can let "infinity" be some typical value that occurs in theories of finite or infinite elliptic curves, or in extended real or complex numbers, etc.. So we let [math]\infty = \{ \{0\}\} [/math] and see how this goes. Note that
[math]\infty [/math] has size 1 by this definition.

>https://www.wolframalpha.com/input/?i=infinity
>>>Infinity is an unbounded quantity greater than every real (and every whole) number.
An "unbounded quantity" means a set that has no maximal element. Our set [math]\infty[/math]
has only one element, which then has to be its maximal element. So Wolfram does not include those examples of infinity that are actually used.

>https://www.wolframalpha.com/input/?i=quantity
>>>a Quantity is how much there is or how many there are of something that you can quantify

Our infinity above has exactly one element. But 1 is not greater than every real number. So the description is wrong.

>Infinity is a concept made up by retards, for retards.
Let us agree that, apart from the fact that it is not "a concept", it does confuse the retards.

[Anonymous No.11614118]

>>11613109
If it's not the same then what is the difference ?
Well it's 0, but I just assume the concept of nil is way beyond your reach.

[Anonymous No.11614122]

>>11614079
I agree, decimals are not real numbers.
[math]\frac{1}{3} and \frac{9}{10}[/math] are clearly real numbers with real parts 1, 3, 9, and 10.

0.333... and 0.9 are just gibberish. Not real numbers. You can't count "0.3" of something.

[Anonymous No.11614125]

>>11613207
Yep, it's the limitation of our writing system; if we were using base 12 1/3 would be 0.4

[Anonymous No.11614168]

>>11614106
>Our infinity
your pulled-out-of-ass infinity
read a book

[Anonymous No.11614176]

>>11614122
30 cents
>wipes sweat from forehead

[Anonymous No.11614195]

>>11614176
>thirty
>30 = 0.3
burger education

[Anonymous No.11614204]

>>11613031
>0.999... is meaningless.
Nah, it's [math]\sum_{n=1}^\infty \frac{9}{10^n} = 1[/math]

[Anonymous No.11614211]

>>11613109
Let x = 0.999...
10x = 9.999...
9 + 0.999... = 9.999...
9 + x = 10x
10x - x = 9
9x = 9
x = 1

[Anonymous No.11614226]

>>11614195
hurr durr

[Anonymous No.11614326]

>>11613977
Indeed. It's clearly meant to be a steam train in this analogy.

[Anonymous No.11614364]

>>11614026
https://en.wikipedia.org/wiki/Point_at_infinity

[Anonymous No.11614563]

>>11614204
This is not an algebraic expression though, just another way to express the same

[Anonymous No.11614565]

>>11614054
>define 0.999... to be 1
>therfore 0.99... = 1
fuck off

[Anonymous No.11614888]

>>11614565
Bullshit. They defined what a decimal expansion is in terms of infinite series. There's nothing wrong with the definition, other than it making your ignorant feelings hurt.

[Anonymous No.11614973]

>>11612986
Consider the sequence of continued fractions:
[math]0.9 = \frac{1}{1+\frac{1}{9}}[/math]
[math]0.99 = \frac{1}{1+\frac{1}{99}}[/math]
[math]0.999 = \frac{1}{1+\frac{1}{999}}[/math]
[math]\cdots[/math]
[math]0.9... = \frac{1}{1+\frac{1}{9...}}[/math], this is, [math] 0.9... = \lim_{x\to\infty} \frac{1}{1+\frac{1}{x}} [/math]

[Anonymous No.11615337]

>>11614563
Well that's what the decimal notation means

[Anonymous No.11615349]

>>11614888
>I define 1 to be 2
>Therefore 1=2
This is what onetards sound like

[Anonymous No.11615357]

>>11614973
So, in order to assert:
[math]0.999... = 1[/math]
you must first assert:
[math]\frac{1}{∞} = 0[/math]

okay

[Anonymous No.11615381]

>>11615357
>>11614009

[Anonymous No.11615399]

>>11613074
Yep.
http://aynrandlexicon.com/lexicon/infinity.html

[Anonymous No.11615413]

>>11612986
Your days of HERESY are all but finished now, SODOMITE! The CRUSADE for finite and discrete mathematics is indefatigable, undefeatable. We of the ONE TRUE FAITH shall emerge victorious. Because we have GOD on our side!

0.999... does NOT equal 1

Even a child understands that until they are brainwashed, coerced, forced into SATANIC HERESY. You corrupted your own daughter,and for that heinous SIN you will burn in the finite fires of HELL

DEUS VULT!

[Anonymous No.11615424]

>>11615413
>wall-of-text schizo

[Anonymous No.11615425]

>>11615381
Not using Surreals, it isn't.

[Anonymous No.11615429]

>>11614565
This so much, only those brain-dead fuckwits cant even see the pants-on-head retarded nature of their own fallacious thinking. They are truly cretins.

[Anonymous No.11615444]

>>11615424
You call that a few lines a "wall of text"?

Man, just wait until you have to read a textbook. Oh wait. Stupid motherfuckers cant into reading.

[Anonymous No.11615453]

>>11613031
i believe 0.999... = 1 was used in the first proof that the transcendentals are uncountable if im not mistaken

[Anonymous No.11615487]

>>11612986
Nobody can conceptualize infinity
It's about understanding the consequences

[Anonymous No.11615555]

>>11615444
get it published then

[Anonymous No.11615766]

>>11615487
>Nobody can conceptualize infinity
source: my ass

[Anonymous No.11615770]

>>11615766
do it big boi

[Anonymous No.11615774]

>>11614122
>You can't count "0.3" of something.
you can't count 3/10 of something ?

[Anonymous No.11615786]

a set X is finite if every injective mapping X -> X is also surjective
a set X is infinite, it is not finite

that wasn't too hard

[Anonymous No.11615792]

>>11615786
lysol or clorox injective?

[Anonymous No.11616347]

>>11614007
Real analysis is easy and only baby retard highschoolers like you suck your own dick off for knowing it.
The problem with Real Analfist is that it forces you to actualize infinity thanks to Gayfag Cantor.
But you wouldn't understand the philosophical implications, all faggots like you know is how to construct the reals (and only once these very Jewish axioms have been accepted). Muh Dedekind butts! Muh Cauchy suhquhnsuss!!!

[Anonymous No.11616365]

>>11616347
>philosophical implications
well, the scientific implication is that we can build spacecraft and shit
so hit me with your hardest philosophical implication

[Anonymous No.11616413]

>>11616365
>thinks we need real analysis to build things
behold the math freshman

[Anonymous No.11616435]

>>11616413
>thinks we don't need the whole theory, just the applicable results of the theory
behold the retard

[Anonymous No.11616494]

>>11616365
>"accept that there are orders of infinities, or you can't build stuff"
You can do all of that without reals, mongoloid.

[Anonymous No.11616498]

>>11612986
And you're typing this up furiously on reddit while cumming just at the thought of the down's anons on here getting their minds blown, yes?

[Anonymous No.11616501]

>>11616435
You think physicists and engineers care about your epsilon delta autism? I know you feel like a big boy because you know proofs now, but sit down bitch

[Anonymous No.11616530]

this philistine is going to say π=3

[Anonymous No.11616827]

>>11616501
>You think physicists and engineers care about your epsilon delta autism?
of course they don't. how is that relevant ?

[Anonymous No.11616887]

>>11615413
How are you even defining 0.999... if you reject the notion of infinity? With that logic you should be calling 0.999... a meaningless symbol. To compare 0.99... with 1 means you accept 0.99... is defined but I doubt it is in whatever system of axioms you're using. You don't even know how to be a finitist.

[Anonymous No.11616913]

>>11613109
This post went full schizo

[Anonymous No.11617070]

>>11615357
Well tell me what you get after slicing your pie an infinite number of time.
I'll wait.

[Anonymous No.11617339]

>>11617070
Kicked out of the bakery?

[Anonymous No.11617354]

ITT: Retards that think they're being clever mathematicians by asserting that, as a number, 0.9999...=1.

NO

Ask your uni professors, only the LIMIT of 0.999... =1. The infinite sequence itself never equals one for any step.

[Anonymous No.11617373]

>>11617354
>Ask your uni professors
pretty sure they will tell me that 0.999... IS the limit

[Anonymous No.11617414]

>>11617373
Ellipses were never used to infer a limit -anything contrary to that is the fault of embarrassed mathematicians changing the definition because someone made them look a fool.

An Ellipse just means (pattern continues). Without a limiting pair, it continues indefinitely in one direction.

[Anonymous No.11617434]

>>11617414
DIS

end the fucking thread before i shoot up cum in this bitch

[Anonymous No.11617446]

>>11617414
>Ellipses were never used to infer a limit
not true at all, lmao

[Anonymous No.11617448]

>>11612986
I don't like flawed notation. I like notation which maps losslessly and unambiguously to the underlying absolute. I see this as a flaw.

Also, infinity isn't real. It is unlikely there is infinite subdivision or extent of any object which exists. Therefore, infinity is a nonsense concept.

[Anonymous No.11617474]

>>11617448
>Also, infinity isn't real. It is unlikely there is infinite subdivision or extent of any object which exists. Therefore, infinity is a nonsense concept.
it is unlikely that there are two completely identical objects which exist. therefore, equality is a nonsense concept.

[Anonymous No.11617579]

>>11613042
No its not. Its a lie you believe.
By your own evidence they are not equal.
If it proves anything it proves that math is a lie.
But then so are tools, dreams and constructions.
Nature does not lie, nature needs no tools, dreams or constructions.
Nature exists as law.
Math is not law.
Only nature is law.
You are confused as to what is true and what is not true.

[Anonymous No.11617721]

0.999..= 1 cannot be true outside of calculus.

Take a sphere with an infinite amount of points and subtract any amount, the state of the sphere is not equal to it's previous state.

[Anonymous No.11617729]

>>11617721
But it still has an infinite number of points, just with a discontinuity at the one you removed.

[Anonymous No.11617731]

>>11617474
Whether you can, at one instant, have two objects existing in precisely the same state, is another matter. I don't know the answer to that.

[Anonymous No.11617737]

>>11617731
neither you know the answer to whether "there is infinite subdivision or extent of any object which exists"

[Anonymous No.11617738]

>>11614211
>9 + x = 10
>nigger you call that a proof?

[Anonymous No.11617755]

>>11614204
that's wrong
a limit of it is 1

[Anonymous No.11617771]

>>11615413
based schizoposter

[Anonymous No.11617778]

>>11617729
Doesn't matter, the state of the sphere is not the same as it was. You can remove any amount and the result is the same, you are left with a difference that exists.

[Anonymous No.11617793]

>>11617778
and what exactly is the analogy with 0.999... supposed to be ?

[Anonymous No.11617797]

>>11613087
yes, it's less by ZERO

[Anonymous No.11617800]

>>11617755
and 0.999... is defined to be this limit

[Anonymous No.11617808]

>>11617800
nigger
0.999 is the infinite sum and 1 is it's limit

[Anonymous No.11617817]

>>11617808
>0.999 is the infinite sum
source: my ass

[Anonymous No.11617818]

>>11617737
-Shrug-
What can you do.

[Anonymous No.11617819]

>>11617793
You can break the sphere (1) into an infinite amount of points. If you believe that removing any amount of points is not reducing the original state of the sphere that is a paradox.

[Anonymous No.11617823]

>>11613977
>NNNOOOOOO INFINITY IS ALREADY COMPLETE, WE HAVE A SYMBOL FOR IT
>"Your naive cartoon vision of a diesel engine chugging along is ridiculous. Embarrassing even."
What's embarrassing is that you saved your retard-tier post and sit on /sci/, waiting for threads like this to post it in:
>>/sci/?task=search&ghost=&search_text=chugging+along
What a sad life lmao

[Anonymous No.11617824]

>>11617819
and how is that relevant to 0.999... being or not being 1 ?

[Anonymous No.11617829]

>>11617800
defined by retards that have egg on their face

0.999... just means 0.999 followed by an infinite number of 9s. It does NOT mean "the smallest number that is greater than any sum featured in the set 0.999..."

[Anonymous No.11617833]

>>11614018
0.0 is a terminating sequence, retard. Consider any number that you enumerate as the result of a mechanical calculator. This is what happens when the result is infinite, there is no termination:

https://www.youtube.com/watch?v=OFJUYFlSYsM

[Anonymous No.11617834]

>>11617824
I don't know how I can make it clearer to you. If you remove any amount of points from a sphere with infinite amount of points, how many points are you left with? And what happens if you add it back in?

[Anonymous No.11617858]

>>11617834
>how many points are you left with?
that depends on how big is the set of points you removed
>And what happens if you add it back in?
you get the sphere back

[Anonymous No.11617881]

i have a cube. it is a geometric cube, I like this cube.

I cut my cube in half, because I like thinner shapes more. Now its' volume is 1/2 what it used to be.

I would like the volume even smaller, so I shall do that again. It is very thin now, at 1/4 what it used to be.

I shall continue to do this, forever.

The intelligent people who want there to be a distinction between 0.999... and 1(Even though, in the common mathematical notations, there actually isn't) will say the result is a 2d square.
Those who think 0.999 = 1, and therefore 1/inf = 0, will say that you are left with nothing.

[Anonymous No.11617883]

>>11617858
Remove any amount you want, what is the numeric representation of removing any amount you pick from a sphere with infinite amount of points?

[Anonymous No.11617893]

>>11617883
>numeric representation
as in terms of cardinal numbers ?

[Anonymous No.11617894]

>>11617819
>You can break the sphere (1) into an infinite amount of points
that is wrong under euclidean geometry. A circle is not a bead necklace, and a sphere is not an infinite number of points.

[Anonymous No.11617904]

>>11612986
no it doesn't and i can prove that.
A.1: .999...!=1
Looking... Looking... No contradictions.
Q.E.D
xD

[Anonymous No.11617920]

>>11616827
>h-h-how is that relevant??
see:
>>>11616365
>>well, the scientific implication is that we can build spacecraft and shit
Your whole argument was that it was impossible to do anything in the world without modern real analysis
>>11613977
>>11614018
>the length is aleph_0 from the get go.
>get go
cringe
>static static static
Please stop using that word, you're an imbecile.

[Anonymous No.11617956]

>>11617920
>>stop using that word
>t. i have no argument

[Anonymous No.11617966]

>>11612986
The answer is clearly in the 6.
1/3=.333...
And .333... × 3 = .999... (on the knife)
However
1/6 = .16666667
And .333 + .167 = .5 = 1/2

[Anonymous No.11617967]

>>11617920
You're a retard who thinks quibbling about, and criticizing word choice is a sign of intelligence. Fuck off.

[Anonymous No.11617969]

>>11617823
LMAO
actually spending your life doing warosu searches

[Anonymous No.11617972]

>>11617920
>Your whole argument was that it was impossible to do anything in the world without modern real analysis
physicists and engineers don't need to know real analysis to use tools provided by real analysis