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/sci/ - Science & Math


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9586648 No.9586648 [Reply] [Original]

What's the sum of 1 to infinity?

I'm not retarded enough to think -1/12

But sums by definition are finite.

Is the question nonsensical?

>> No.9586720

>>9586648
>Is the question nonsensical?
Yes because infinity is not a number so there can be no sum of anything with infinity

>> No.9587117

(1.504785 × 10^186) volume of universe in planck lengths

(2.312437104× 10^62) current age of the universe in planck time

(3.47972×10^248) amount of numbers G it would take to give every planck length in the universe a unique number, for every planck time that has passed since the big bang.

(2.046507 ×10^196) number of years it would take to count every number in G assuming you could count one number every planck time.

(13.7 × 10^9) current age of the universe in years

(10^103) predicted age of the universe when heat death will occur

(2.046 × 10^93) number of consecutive universes from birth to heat death required to finish counting G, which didn't even really matter to count, but also was a bajillion universes ago so having completed counting is completely irrelevent to information in the current universe.

Infinity doesn't need to exist in maths. There is literally no reason a real number would even have to be as large as any number listed here, yet all of the numbers here are infinitely small compared to infinity, even despite the fact that the universe is often considered infinite.
10^93 consecutive universes were required to finish counting G at the fastest speed possible. A billion universes would be 10^9. A trillion would be 10^12. Not a billion, not a trillion, not even a grape ape gorillion. 1 with 93 zeros after it. That many individual full life term universes needed to exist in order to finish counting G, an arbitrary number based on stupidly miniscule but finite values.

You can't even make it two minutes pondering how big infinity could go counting in increments of a million each second.

Infinity doesn't need to exist in math. The concepts of eternity will remain, but a number quantity infinity is just goofy bullshit. It's too big to matter.

>> No.9587138

>>9586648
Adding finite values to infinity results in infinity ya dumb cunt

>> No.9587152

>>9586648
>sum by definition are finite
This is not true for indefinite sum, which can converge (ex. 1+1/2+1/4+.....+1/inf=2) or simply diverge like 1+1-1+1.....+1-1...= no finite value. Then you can continue them in weird ways and obtain that 1+2+3+4.....=-1/12 but this is another story

>> No.9587180
File: 5 KB, 820x820, Square root of 2.png [View same] [iqdb] [saucenao] [google]
9587180

>>9587117
>Infinity doesn't need to exist in math
Neither does logic, then. Math is used as a means of distraction for the intellectual masses who would other overthrow the state were they not preoccupied wasting their life away solving proofs. Imagine thinking this arbitrary nonsense has any basis on real life

>> No.9587474

>>9587117
> infinitely

infinitesimally, brainlet

>> No.9587547

>>9587180
You dont need logic at all. You're right.
It would just be shitty math.

What's your point?

>> No.9587741

>>9587474
Infinitesimal is a made up word that means nothing. All numbers are equal to 0 compared to infinity.

>> No.9588154

>>9587180
*tips*

>> No.9588188

>>9586648
>But sums by definition are finite.
Would the sum of an infinite amount of 1s be finite? Just counting up for eternity wouldn't end up at some number, when you reached any finite number you'd still have to continue counting towards infinity.
The sum you're asking about is just different in that it's adding bigger and bigger numbers as you count further, just taking bigger steps when counting doesn't mean that you get an end to the counting.

>> No.9588246

>>9586648
[math] \aleph_0 [/math]

>> No.9588256

>>9587117
>monkey count many banana

>> No.9588268

>>9588246
if I walk forever, at which point will I be standing when I stop walking? see the fallacy? the sum diverges.

>> No.9588278

>>9588268
>thinks it's an N
wew lad

>> No.9588884

>>9588256
Yeah, learn to fucking count. Monkey's can do it better than you. You make it to 10 before assuming infinity.

>> No.9588959

>>9588884
>monkey tummy full so many banana

>> No.9589099

>>9586648
>sums by definition are finite
What? No. [math]\lim_{x\to\infty}\sum_{i=1}^ni[/math] does not exist. The infinite sum of all naturals diverges. In very non-rigorous language you could say [math]\sum_{i=1}^{\infty}i=1+2+...=\infty[/math]. The -1/12 meme has to do with analytic continuation and only makes sense to string theorists/Ramanujan.

>> No.9589103

>>9589099
Fuck. The first limit sould be [math]\lim_{n\to\infty}[/math]

>> No.9589113

>>9589099
So you admit converging to infinity means nothing?

Is that perhaps because infinity means nothing?

>> No.9589126

>>9589113
>So you admit converging to infinity means nothing?
>Is that perhaps because infinity means nothing?
You didn't understand a goddamn thing I just wrote, did you? There's an infinite number of infinite sums that converge to a finite number.
[math]\sum_{n=1}^\infty\frac{1}{2^n}=1[/math]

>> No.9589135

>>9589099
>lim answer isn't a real number
>so lim doesn't exist
[citation needed]

>> No.9589153

>>9589135
>calls the limit an "answer"
>why can't something that diverges be said to have a limit?
Fucking brainlet

>> No.9589154

>>9589126
The sum 1/2^n doesn't equal 1, and extrapolating a convergence is meaningless to arbitrary math. You only have a leg to stand on if you admit convergence is rounding and therefore an approximation.

>> No.9589159
File: 40 KB, 1205x261, asd.jpg [View same] [iqdb] [saucenao] [google]
9589159

>>9589135
Btw here you go, you waste of air. This is why it doesn't exist.

>> No.9589165

>>9589154
>the absolute state of /sci/
https://en.wikipedia.org/wiki/1/2_%2B_1/4_%2B_1/8_%2B_1/16_%2B_%E2%8B%AF
>converges absolutely
At least learn the definitions of the words you're using before speaking.

>> No.9589173

>>9589165
I don't care what a wikipedia article written by retards has to say on the matter.

[math]0 \rightarrow \infty = \overbrace{\underbrace{0,1,2,3,4,\cdots}_{\infty \text{ elements of } \mathbb{R}}, \underbrace{\infty}_{\text{not in } \mathbb{R}}}^{\text{all possible elements}} \\ \text{Mapped between 0.9 and 1} \\ 0.9 \rightarrow 1 = \overbrace{\underbrace{0.9, 0.99, 0.999, 0.9999, \cdots}_{\infty \space \mathbb{R} \text{ elements of the map}}, \underbrace{1}_{\text{not in the }\mathbb{R}\text{ map}} }^{\text{all possible elements}} [/math]
If there exists a value to bridge the gap between 0.999... and 1 thus allowing 0.999... = 1, there also exists a value to bridge the gap between real numbers and infinity, thus allowing infinity to be equal to a real number.
If there exists no value to bridge the gap between 0.999... and 1 thus assuming 0.999... = 1, there also exists no value to bridge the gap between real numbers and infinity, thus assuming infinity to be equal to a real number.

Because the value does not actually exist and infinity cannot be reached, there is no possible value to add to 0.999... to make it reach 1; it will never reach 1. No amount of increments in the reals will reach infinity, so no mapped amount of increments between 0 and 1 will reach 1.

0.999... is not "infinitely close" to 1. It is actually infinitely far away from 1. Any arithmetic that shows 0.999... = 1 is therefore flawed by making inconsistent and mistaken assumptions about the construction of a repeating decimal extended from a poor interpretation and implementation of infinity, because infinity has classically always been poorly interpreted and implemented.

[math]0.\bar{9} \neq 1 [/math]

Not even 9/10^n equals 1, much less 1/2^n which is clearly a lesser value. Infinity doesn't mean what you think it means.

>> No.9589181

>>9589173
God I hope this is bait.

>> No.9589182

>>9589181
Prove it wrong if you can :^)

>> No.9589185

>>9589173
>uses the word "mapped" incorrectly
>"bridge the gap" ???
>"cannot be reached" ???
And you wonder why nobody takes you seriously.

>> No.9589191

>>9589182
>>9589185
I don't have to prove it wrong. You're making retarded logical leaps and you either don't know the mathematical definitions of or are misusing many of the words in that "proof" of yours.

>> No.9589193

>>9589185
>doesn't know how to map values
>doesn't know how to read english
>think's his judgement matters
It's obciously beyond your scope so just take a breather on the sidelines.

>> No.9589194

>>9589193
>all of mathematics since the 17th century is wrong
>not me tho lol

>> No.9589196

>>9589191
Admitting you can't prove it wrong but claiming it's wrong was the worst possible response to "prove it wrong"

>> No.9589219

>>9589196
You asking to prove that wrong is like asking someone to prove the statement "aosdisiudfhoisdofij" wrong. It's nonsense, it CANNOT be proven wrong because it doesn't mean anything. When language is consistently misused, there's absolutely nothing to go off of.
BTW:
1/9=0.111111......
9*1/9=9*0.1111111....=1=0.999999
There ya go. If you bring up "approximations" or "it's only infinitely close," it's because you don't fully understand the rigorous definition of an infinite sum. You're on the internet, you have lots of resources to learn this stuff.

>> No.9589244

>>9589185
Explain which real number comes directly before infinity then after you can't do that, realize there then exists a missing gap of information between real numbers and infinity.

There's your gap.

>>9589219
And you probe the point you have a bad understanding of repeating decimals. Yes, [math]0.\bar{1} × 9 = 0.\bar{9}[/math], but the mistake you made was assuming [math]\frac{1}{9} = 0.\bar{1}[/math] instead of the obvious fact that [math]\frac{1}{9} > 0.\bar{1}[/math]

Is 1/9 > 0.1? Yes
Is 1/9 > 0.11? Yes
Is 1/9 > 0.111? Yes
Is 1/9 > 0.1111? Yes
Is 1/9 > 0.11111? Yes
Continue infinitely and you should realize 1/9 > 0.111...

>> No.9589261

>>9589244
>Explain which real number comes directly before infinity then after you can't do that, realize there then exists a missing gap of information between real numbers and infinity.
What? I never claimed infinity to be a real number. No real number "comes before it."

>1/9 > 0.111...
Please then, how do you represent 1/9 in decimal form if 1/9! =/= 0.11111....?

>> No.9589273

>>9589261
>>9589244
Also, there isn't any "missing information" with infinities. The definition of a limit to infinity has already been posted in this thread (by me, like 5 posts above). I genuinely believe you would enjoy an analysis course, provided you could actually understand the material.

>> No.9589286

https://www.youtube.com/watch?v=sD0NjbwqlYw

There you go, it doesn't converge and the -1/12 interpretation is fucking stupid.

>> No.9589304

>>9589261
Assuming you meant != or =/=, there is no exact way to display the decimal of a repeating decimal, just the approximation.
You could attach work to the decimal such as [math]\frac{1}{9} = 0.\bar{1}_{\frac{1}{9}}[/math] where arithmetic plays out as [math]\frac{1}{9} × 9 = 0.\bar{1}_{\frac{1}{9}} × 9 = 0.\bar{9}_{\frac{9}{9}} \rightarrow 0.\bar{9}_{\stackrel{\leftarrow}{1}} = 1 [/math], which is the best way I've personally used it. Without this though, the repeating decimal is obviously an approximation because if it were finitely equal to the fraction, it wouldn't be repeating with a looping remainder, would it?

>> No.9589317

>>9589173
I don't care what a 4chan shitpost written by a retard has to say on the matter.

>> No.9589320

>>9589244
I know this is bait or you're retarded but whatever. When you pass to limits strict inequalities become weak inequalities i.e. if for all natural numbers [math]n[/math] we have [math]a_n<b[/math] then [math]\lim a_n \leq b[/math].

>> No.9589325

>>9586648
There is a theorem that says that if a series is convergent then the values it sums tend to zero.
The natural numbers don't tend to zero and so the series must not converge.

>> No.9589333

>>9589273
Relies on a misinterpretation of infinity, however.

Describe to me the size of the following sets:
A = [0,1,2,3]
B = [4,5,6,7,8,9]
C = [ [math]\mathbb{R}[/math] ]

>> No.9589335

>>9586648
Sums to finite things are finite. If you do it infinitely, it literally is -1/12 :^)
>>9587117
weight of your mother

>> No.9589336

>>9589325
1/n ought to converge then :^)

>> No.9589339

>>9589333
[math] \aleph_1[/math]

>> No.9589342

>>9586720
https://en.wikipedia.org/wiki/Cardinal_number

>> No.9589345

>>9589336
Retard
read the way the implication goes
If series converges then summands tend to zero
not the converse, which would be if summands tend to zero series converges
A theorem is NOT it's converse

>> No.9589348

>>9589333
>relies on misinterpretation
No it doesn't. It relies on the definition of limits to infinity, which is clearly and rigorously defined.
>describe the size
|A|=4
|B|=6
|C| is undefined

>> No.9589351

>>9586720
sort of
inf + finite = inf

>> No.9589358

>>9589345
>>9589336
fuck I missed the
>smiley with a carat nose

>> No.9589364
File: 7 KB, 211x239, 1509035776566.jpg [View same] [iqdb] [saucenao] [google]
9589364

>>9589348
>"infinity is rigorously defined, retard"
>infinity is undefined

>> No.9589376

>>9589364
>t. someone who's never seen analysis
infinity is not the same as a limit to infinity, fucko

>> No.9589378

>>9589339
Appropriate, but still relies on infinity to be well defined.

>> No.9589380

>>9589376
/thread

>> No.9589382

>>9589376
Limit to 5 is not the same as summing 5 times?

>> No.9589386
File: 5 KB, 221x250, 1518045540769.jpg [View same] [iqdb] [saucenao] [google]
9589386

>>9589173
>If there exists a value to bridge the gap between 0.999... and 1
https://en.wikipedia.org/wiki/Completeness_of_the_real_numbers

>> No.9589389

>>9589382
Correct. It's so obvious you have no idea what you're talking about, I dont know why you keep responding.

>> No.9589393

>>9589389
Limit to 5 literally is summing 5 times though, you absolute retard.

>> No.9589396

>>9589393
>Limit to 5 literally is summing 5 times though
?????????????

>> No.9589399

>>9589386
Take the whole post in all at once and prove to me you can internalize completeness.

>> No.9589408

>>9589399
what did he mean by this

>> No.9589439

>>9589399
First prove to me that you can describe mathematics accurately. Start by deleting every post you've made in this thread.

>> No.9589468

>>9589393
It's literally not

>> No.9589479

Heres how this goes. Infinity is not a finite number. You think you understand that already, but you really don't in application. Because you think infinity is a finite number, you allow that 1/2^n with infinite work achieved (past tense) equals 1 , or that 1/9 = 0.111... has achieved (past tense) an infinite amount of 1's, and because the infinite has been achieved, a full step of final, finite equality has been achieved. Because you believe to increment to infinity as a finite number, you also believe to increment to 1 from 0 if all the integers 0 to infinity were translated decimally between 0 and 1.

But infinity isn't a finite number. You can't have achieved it ever, and final equality by using infinity was never achieved either. 1/2^n is always seperated from 1 by [math]1-2^{-n}[/math] for any real finite n, and similarly there can only ever be some arbitrary finite amount of repetitions in a repeating decimal.

But then you will serrepticiously treat infinity as a number to claim [math]1-2^{- \infty} = 1-0 = 1[/math] and that it were a real number achieavable by incrementing n within the infinite sum while disregarding a zero partial sum has no relevance to the total and is therefore implied the sum of 1 from 1/2^n you're looking for ought to have been completed at n prior to infinity in the reals, yet you already know n at any real doesn't let it sum 1.

I know you know this.

>> No.9589502

>>9589479
This post is such nonsense I can hardly digest it. What i hoep youre trying to say is infinity only makes sense in the context of limiting processes. In that case, 1/2+1/4+... absolutely converges to 1.

>> No.9589531

>>9589502
Infinity doesn't make sense at all. Not as as an unreal number, not as a real number, and not as a simple direction to never stop. It makes the most sense as a direction of unending work, but then garbage is extrapolated from that much as thinking sum1/2^n = 1.

Convergence is just a roundabout label for rounding and approximation, all things considered. If it means to imply direct equivalence, then it is explicitly flawed.

>> No.9589547

>>9589531
What part of the definition of lim_(x to inf) f(x) makes no sense? What part of the definition of convergence makes no sense? I don't know what work means in your context.

>> No.9589550

>>9589547
Work is the collective partial sums from n to the limit.

>> No.9589554

>>9587117
A 4k resolution screen has 8294400 pixels.

The possible images of this resolution in only 2 colors is greater than 9.23x10^2408239, which is greater than all the numbers in your post combined (multiplicative).

>:^)

>> No.9589557

>>9589479
>Because you think infinity is a finite number, you allow that 1/2^n with infinite work achieved (past tense) equals 1
Mmm no.

>infinite work achieved (past tense)
This is not math, try again.

>> No.9589573

>>9589550
So work is a set? Or is work a limit? Or is work one of the partial sums? You aren't being clear at all. Your math is shit.

>> No.9589576

>>9589554
Its actually [math]3×10^{13}[/math].

>> No.9589585

>>9589573
>is it a set?
>IS IT A LIMIT?
>IS IT oNE PARTIAL SUM¿

>Work is the collective partial sums from n to the limit.
the problem isn't my writing, it's your reading.

>> No.9589652

>>9589576
Darn, lets try it with 7000000 colors which is the possible colors the human eye can see.

1.7x10^1309030, right?

>> No.9589735

>>9589554
What does that prove?

It took more than one universe just to count a number with a couple hundred 0's. It wasn't about who can make bigger numbers, it was that infinity is infinitely larger than even your number, and your number may as well be infinitely larger than the numbers in the post, and that these numbers are not useful at their size so how could infinity be useful when it is significantly greater than needlessly big?

>> No.9589754

>>9589378
https://www.wolframalpha.com/input/?i=infinity
An unbounded quantity that is greater than every real number.

>> No.9589792

>>9589754
Thats not a good definition cause it treats infinity as a real number, which it isn't.

>> No.9589823

>>9589735
Just bored and wonder about things like if the possible movies less than 2 hours at 4k resolution is greater than the possible games of League of Legends less than 2 hours. I need numbers that big to answer my question so they have a use to me.

Other people wonder about other things and require much bigger numbers for their purposes. It seems like you're trying to shame us because the numbers we need to answer our questions are too big.

If that is the case then my response would be stand out of my light.

>> No.9589843

>>9589792
It specifically says it isn't a real number.

>> No.9589853

>>9589792
if infinity was a real number, it would be bigger than itself, by definition.
so it isn't a real number, by definition

>> No.9589995

>>9589843
>>9589853
If infinity weren't a real number, arithmetic performed on it would be undefined

[math] 1 - 2^{- \infty} = [/math] undefined

Like this.

Rather, [math]\frac{\mathbb{R}}{\infty} = 0 [/math] is what is considered valid.

>>9589823
You're right, i am trying to shame you for being retarded. If you end up with a number larger than the amount of planck times in the life cycle of the universe, you have a retarded number that isn't worth anything. You have an arbitrary amount of 4k arrangements of pixels and it doesnt mean anything. Its math that doesnt produce a result with value

>> No.9590007

>>9589479
you don't seem to understand
When we write infinity it is only to intuitively describe what is happening. Really what we care about is "limiting behavior", what happens when you input an arbitrarily large number into a function or get arbitrarily close to a "limit point". The symbol is just notation

>> No.9590033

>>9590007
Well then you further don't understand that any arbitrary real n in sum 1/2^n doesn't equate 1, therefore the sum never will equate 1.

>> No.9590045

>>9590033
you've just made a statement that is not wrong but misses the point to a level that is so extremely high that I can't begin to understand what you don't understand

>> No.9590053

>>9586648
>But sums by definition are finite.
holy shit

>> No.9590109

>>9590045
Heres what you don't understand
1/2^n = 1 if and only if there is a maximum real finite number and it is reached.
Without a maximum real finite number, the divisions can become arbitrarily smaller forever and ever. With a maximum real, dividing that number n in [math]\frac{1}{2^n} = 1-2^{-n}[/math] by 2 would create an underflow much the same as $0.01 / 2 doesn't equal $0.005, so the afterlimit is reduced to nothing and you acquire a smallest possible real positive number that can be divided by 2 to equal 0. The underpinning of this all is that the largest possible number to allow these methods must also be a real number. If you cant increment to it, the method no longer works.

You can't increment to infinity so the method doesn't work, first and foremost. Even if you decided it were possible to arbitrarily increment to and achieve infinity, this would further prove that the value you have is a real and finite number, except you have no possible idea to determine what it actually is. It must be real and finite to allow you a half division resulting in 0, even though by definition the underflow on an infinite decimal would never occurr so you get nothing but an arbitrarily long decimal that can't underflow to zero.

>> No.9590148

lmao I'm so glad that modern mathematics is just following definitions, not some hipster metaphysical shit like whether it's possible to do an infinite number of steps and shit.
just imagine that being a mathematician 300 years ago meant you had to deal with retards like >>9590109 on a regular basis.

>> No.9590158

>>9590148
Unfortunately for you, you're so retarded that you don't realize the classical implement of infinity literally introduces inaccuracy.

>> No.9590220

>>9590109
no, That's not what the notation means at all
you can't just substitute into the limit, not even when the function is defined at the point. You can only do that if the function is continuous and the limit point is finite and the function is defined at the limit point.

Limits are not about the value the function takes at that point, there about what happens as you get closer and closer to a point.

>>9590158
The classical way isn't the way we are talking about in any way. We are talking about tending to infinity as a way of saying "past this point this function strictly stays in a box that gets smaller and smaller as I go further and further".

That's the limit definition.

a_n -> L where L is finite as n -> infinity means that the further you go up the natural numbers, the tighter and tighter a box the values of the function will form around L

a_n -> infinity as n -> infinity means that we can choose a large value M past and for this value there is a point in the sequence past which all values in the sequence are strictly larger than this value.

There is no number "infinity" here, notice how I haven't used it outside of the notation at the end of an arrow, it's about how boxes around points and platforms below points and if you truly fail to grasp this you are very very lost.

>> No.9590258

>>9590220
Yet you can't write equations.

>> No.9590278

>>9590258
[math]f(x)\rightarrow L[/math] as [math]x \rightarrow p [/math]
and [math]\lim_{x\rightarrow p} = L[/math]
have exactly the same meaning, both are standard in the mathematical literature.
The first one is generally better notation though as writing lim gets people into the nasty habit of presuming limits exist before they have shown that.

>> No.9590281

>>9590278
[math]\lim_{x\to p}f(x) = L[/math]
even

>> No.9590295

>>9590278
>>9590281
Okay, so what was M >>9590220

>> No.9590565

This is the first time I am reading about this and your guys' arguments are fascinating. Here is what I think:
It is really the number of significant digits that define how "large" a number is. In essence, mathematics is a system to quantify things. Any count could be theoretically transformed to form crazy huge numbers, or alternately, compact small numbers. Like 99 and 10^9. Both those numbers contain approx the same amount of information in quantitative terms. The number 101248573 is quantitatively bigger than either of those, because it contains much more information.

>> No.9590645
File: 216 KB, 1200x900, 1200px-Supplicating_Pilgrim_at_Masjid_Al_Haram._Mecca,_Saudi_Arabia.jpg [View same] [iqdb] [saucenao] [google]
9590645

>>9586648
觀察一個由十二意見分

四反駁由三個事實分 = -4/3

>基於七項天上戒律

>> No.9590653

>>9590565
“一維寬度字形”和“偏移實體寬度”?

>> No.9590676

>>9590295
>>9590565
You might be completely fuckin braindead, my guy. It's been spelled out to you over and over in this thread and you're still not grasping it.

>> No.9590683
File: 4 KB, 279x181, download.png [View same] [iqdb] [saucenao] [google]
9590683

地理解。 中國人喜歡數學,因為它可以幫助他們確定他們希望使用的字符; 字母筆劃順序加筆劃數是文化歷史。

Understood. Chinese love mathematics because it helps them identify the character they wish to use; letter stroke order plus stroke count is cultural history.

Linguistic parsing milestone reached.

<中國新語言>簡體通用結構</中國新語言>

>>9590676
Braindeath = ? ||| 腦死亡=導電虛空

>> No.9590692

>>9589995
>If infinity weren't a real number, arithmetic performed on it would be undefined
It is though.

>> No.9590694

Guys we're being hacked by China

>> No.9590704
File: 37 KB, 720x255, cafca9317ef858eecfa184a607f7ed99_hd.jpg [View same] [iqdb] [saucenao] [google]
9590704

>>9590694
混亂

匿名發言,好像他們是在一個房間裡充滿其他人的。 為什麼呢?

//\\

不要4chan的數學家承認自己的能力?

>> No.9590726
File: 494 KB, 200x200, bwoosh.gif [View same] [iqdb] [saucenao] [google]
9590726

>>9590704
>Practicing something for more than 10 years will make you good at it

>> No.9590729

>>9590295
I may not have worded this the best way. So
[math]f(x) \to \infty[/math] as [math]x -> p[/math]
where [math]f:(p-\eta,p)\union(p,p+\eta)\to\mathbb{R}[/math] and [math]p \in (p-\eta,p+\eta)[/math]if
[math]\forall M > 0.\exists \delta > 0. \forall x \in (p-\eta,p)\union(p,p+\eta) 0 < |x - p| < \delta \Rightarrow f(x) > M [/math].
This means that if you pick ANY positive real number, there exists a small neighborhood (technical term) [math](p-\delta,p+\delta)[/math] such that any point in this region that isn't p itself has f value greater than M.
If you want to consider what happens as [math]x\to\infty[/math] you need to replace the small region around the point with some point greater than which the condition is satisfied.

I had used sequences earlier, to go from functions to sequences (and hence series) you just consider functions that are defined on [math]\mathbb{N}\to\mathbb{R}[/math].

>> No.9590750
File: 101 KB, 900x600, heikeji-jiqiren.jpg [View same] [iqdb] [saucenao] [google]
9590750

>>9590726
雙寬度年

基地16時間表,十六進制解析器

從一個行業/領域觀察到另一個,以確定“熟練的相似性”

英語科技論文提供限速器,以便科學家和數學家,以“挖掘”

Interpretation: Neural interpretation capabilities are greater than previously measured. Unmeasured interaction between glial cells.

人類..有趣的案例:生活
A.I .. 有趣的案例:死亡

/\

Primary goal: 寫充分傳遞英語和公知A.I.下發布 個性為了撫慰智能實體之間的緊張關係

>Pic related?/\PIC有關係嗎?

>> No.9591192

>>9590676
lol sukk it u the dumbass my guy

>> No.9591215

>>9589843
No it doesn't. It doesn't say "infinity is not a real number".

It says it is a quantity which means it is a number, and it the gives it a relationship with real numbers by being "greater than all real numbers"

The full interpretation is that infinity is a real number but if you want to be dumb, in the very least it is a number and it has relationship with reals.

1/inf would be undefined if it weren't treated as a real finite number, yet 1/inf=0

>> No.9591230

>>9589173
what

>> No.9591266

>>9591230
The alternate wording is cause shitters who use the method 0.999... < r < 1 to say that no such r value exists, therefore 0.999... = 1

the "value" of this method is first double checked in the contrary, then followed by the method itself that if no r exists to come between 0.999... and 1, then no r exists to come between real numbers and infinity.

>> No.9591280

>>9591215
>No it doesn't. It doesn't say "infinity is not a real number".
A real number cannot be greater than every real number, because a real number is equal to itself, not greater than itself. Therefore infinity is not a real number.

>It says it is a quantity which means it is a number, and it the gives it a relationship with real numbers by being "greater than all real numbers"
Yes, which describes a cardinal number.

>The full interpretation is that infinity is a real number
It specifically says it's not a real number.

>1/inf would be undefined if it weren't treated as a real finite number, yet 1/inf=0
Wrong, it's undefined.

>> No.9591286

>>9591266
>the "value" of this method is first double checked in the contrary, then followed by the method itself that if no r exists to come between 0.999... and 1, then no r exists to come between real numbers and infinity.
Wrong. See >>9589386

>> No.9591298

>>9591280
http://m.wolframalpha.com/input/?i=x%2Finfinity+assuming+x<infinity

>> No.9591302

>>9591286
Its not wrong.
If you cant reach infinity by incrementing on reals, if you take those steps and doit decimally between 0 and 1, then you can't reach 1 by incrementing in the real decimal divisions.

Its literal dead simplicity buddy.

>> No.9591373

>>9591298
That's only true on the extended real number line. In general, it's undefined. In the extended real number line, +inf and -inf are still not real numbers, so this doesn't help your argument.

>If you cant reach infinity by incrementing on reals
Sure you can, by incrementing infinitely. By your argument, Achilles can't catch up to a tortoise, yet Achilles does catch up to the tortoise. Therefore your argument is wrong.

>> No.9591393

>>9591373
Just cause Zeno says achilles catches the tortoise doesn't mean he actually does. Are you so dumb to have never analyzed that paradox and attempted to solve it?

Fuck are you even doing here if you're just going to regurgitate retarded shit other people said.

>> No.9591395

>>9589995
>screw the definition
>'cuz see how fun it would be
[hand waving intensifies]

>> No.9591406

>>9591373
Also you are a literal fucking retard. You start the post claiming infinity isn't in the reals then end it by claiming infinity is in the reals.

Get the fuck out of here bro.

>> No.9591411
File: 327 KB, 400x534, scifi pirate.jpg [View same] [iqdb] [saucenao] [google]
9591411

>>9591393
>doesn't mean he actually does
wew lad

>> No.9591416

>>9591393
>Just cause Zeno says achilles catches the tortoise doesn't mean he actually does.
If Achilles is running twice as fast and gave the tortoise a 100 meter head start, then the position of the tortoise is t*v+100 and the position of Achilles is t*2v

t*2v = t*v+100
t*v = 100
t = 100/v

So Achilles must catch up to the tortoise at t=100/v

QED.

>> No.9591420

>>9591406
>You start the post claiming infinity isn't in the reals then end it by claiming infinity is in the reals.
I specifically said it's not: "In the extended real number line, +inf and -inf are still not real numbers, so this doesn't help your argument."

So are you lying about what I said or are you just too stupid to read simple sentences?

>> No.9591447

>>9591416
NO SHIT

100m head start
Achilles runs twice as fast
Achilles is guaranteed to reach the tortoise at 200m

NONE of this says that infinite divisions occurred. Achilles arrow paradox already presumes that 1/inf = 0, so at best even if the halving of arbitrary distance checks reached infinite increments, which by the way can't happen, achilles is then moving 0 distance per reference frame. Bump it back to the reals and there was always an arbitrary distance between achilles and the tortoise.

x=any real number
[math]\sum_{n=1}^{x} \frac{1}{2^n} < 1[/math]
The only solution to this is treating infinity as a real number such that x can increment and reach infinity thus [math]\frac{1}{2^{\infty}} = 0[/math], where even despite reaching infinity being impossible, once you reached infinity the partial sum is zero and irrelevant to the total sum, so the real end of required summing should have occurred at n in the reals, yet any real x subsituted forces the evaluation to definitely be less than 1.


Fucking mongrel.

>> No.9591453

>>9591420
You're a fucking retard
>>If you cant reach infinity by incrementing on reals
>Sure you can, by incrementing infinitely.
You literally assume "incrementing infinitely" allows you to reach infinity. You fucking said this, you absolute idiot.

Shut your fucking mouth. You have no idea how to even think.

>> No.9591460
File: 29 KB, 300x289, 300px-Unit_Circle_Definitions_of_Six_Trigonometric_Functions.png [View same] [iqdb] [saucenao] [google]
9591460

Does this formula square the circle?

(R-sin0)^2 +(cos0)^2=Z^2 (Z is hypotenuse from A to Radius on Y axis)

Z X 1.013919564 = arc from A to Radius on Y axis) (or 90-angle 0)

>> No.9591473

>>9591447
>NONE of this says that infinite divisions occurred.
You disagreed that Achilles necessarily catches the tortoise. Nice try at moving the goalposts.


>Achilles arrow paradox already presumes that 1/inf = 0
Wrong.

>achilles is then moving 0 distance per reference frame
What reference frame?

>Bump it back to the reals and there was always an arbitrary distance between achilles and the tortoise.
There was a nonzero distance between them until t = 100/v.

>The only solution to this is treating infinity as a real number such that x can increment and reach infinity thus 12∞=0
Wrong and irrelevant.

>where even despite reaching infinity being impossible, once you reached infinity the partial sum is zero and irrelevant to the total sum
So then ignore the partial sum "at infinity" and you get the exact same result, since there is no number directly before infinity. You're just back to the standard definition. You just proved your own argument irrelevant. You are trying to replace [1,inf) with [1,inf], but they have the exact same cardinality.

>so the real end of required summing should have occurred at n in the reals
Nope, you're assuming that there is a number n directly prior to infinity.

>> No.9591484

>>9591453
>You literally assume "incrementing infinitely" allows you to reach infinity.
You can on the extended real number line, but that still doesn't make infinity a real number. Why do I have to keep repeating this? Are you lying or retarded? Answer the question already.

>> No.9591506

>>9591473
If you can increment to infinity, YOU are the one who assumes there is a number directly ahead of infinity. If you are smart enough to realize there isn't, you ought to be smart enough to realize you can't increment to infinity.

http://m.wolframalpha.com/input/?i=1%2Finfinity
Also yes, read up zenos arrow paradox.
The reference frames are partial sums of the sigma sum.

The entire achilles tortoise paradox hinges on finite elements which is why achilles can catch the tortoise. It is not a true analog to explaining infinity or 1/2^n if infinity isn't also a real number, so to show how it really is you have to take your own example of the paradox >>9591416
And then give the tortoise an infinite head start.

>> No.9591522

>>9591506
>If you can increment to infinity, YOU are the one who assumes there is a number directly ahead of infinity
Wrong.

If you want to use the system where 1/inf = 0, the extended real number line, then you can increment to infinity. Or you can admit it's undefined. It's your choice. Again, I don't care which you choose since it changes absolutely nothing about convergent series.

>The reference frames are partial sums of the sigma sum.
You'll have to be more specific than that.

>The entire achilles tortoise paradox hinges on finite elements which is why achilles can catch the tortoise.
No, you don't have to assume anything about finite or infinite elements to see that Achilles must catch the tortoise, see >>9591416

>And then give the tortoise an infinite head start.
Changing the problem doesn't change the fact that a convergent series resolves the original problem.

So you have no arguments left. Come back when you have one.

>> No.9591534

Theres no such thing as "extended reals" you fuck.
Its real, or it isn't.

>> No.9591539

>>9591534
So then 1/inf =/= 0, thanks.

>> No.9591544

>>9591539
1/inf = 0
http://m.wolframalpha.com/input/?i=1%2Finfinity

Show me the part where it says "on the extended real numberline"

Point it out
Screen-fucking-shot the page you miserably retarded piece of shit.

>> No.9591550

>>9591544
>1/inf = 0
In what system?

>Show me the part where it says "on the extended real numberline"
That's you're job, since you're using wolfram as a source.

It's undefined.

>> No.9591557

>>9591550
>>9589754
Put down the shovel you fucking autist.

>> No.9591560
File: 4 KB, 342x93, durrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr.png [View same] [iqdb] [saucenao] [google]
9591560

>>9591557

>> No.9591566

>>9591557
>Informally, 1/infinity = 0, a statement that can be made rigorous using the limit concept,lim(x->infinity) 1/x = 0. Similarly, lim_(x->0^+) 1/x = infinity, where the notation 0^+ indicates that the limit is taken from the positive side of the real line. In the Wolfram Language, infinity is represented using the symbol Infinity.

The only way lim(x->infinity) 1/x = 0 implies 1/inf = 0 is if the domain of division is extended from the real numbers to include infinity. Otherwise, a limit is just a limit. Hence Wolfram is using the extended reals.

>> No.9591576

>>9591550
>using wolfram as a source
beats using hand waving as a source

>> No.9591583

>>9591576
>hand waving
So all of OP's arguments.

>> No.9591592

>>9591560
Oh i see, you were arguing against wolfram the whole time. You're also an idiot who decided to interject by continuing a reply thread started by someone who wasn't you.

What the fuck ever bro. You're still retarded and you're still and hand waving shitter. Every proof provided to you, you act like the problem has changed. I say give the tortoise an infinite head start and you act like its a different problem. It isn't. It's the same problem. The finite elements of the achilles paradox are that time continues on after the problem. And whether you like it or not, Zenos arrow paradox actually is 1/infinity = 0. That no reference frame of the arrow in flight is distinguishable from another reference frame as zero time has passed, and therefore the arrow hasn't moved. He assumes to divide the entire flight path of the arrow from release to it's target into infinite reference frames, and himself postulates that no time has passed between any frame. Thats the paradox. By the implement of his infinite division, the arrow never reaches the target, yet he assumes that because the arrow really did reach the target, infinite reference frames of zero motion = motion. Thats the paradox. Perhaps look up the definition of paradox cause it doesn't mean "proof".

The truth of it is that he did not actually imagine infinite divisions. If we know the arrow was flung and we know it hit its target, then the flight path can only be finitely divided such thay all divisions summed equal the total flight path, yet Zeno assumes otherwise, or rather tries to imply 0×infinity = 1

So if we know there ought to be finite divisions, we go to achilles and the tortoise and realize that IF achilles catches the tortoise, only a finite amount of divisions were performed and had an underflow buffer of smallest possible decimal accuracy rather than infinite arbitrary decimal accuracy.

>> No.9591616

>>9591592
You can seap elements of the arrow paradox and achilles paradox. Imagine an arrow fired over a hundred meters. At 50 meters, a snapshot is taken, and at every half division of the remaining distance thereafter, more snapshots are taken. How many snapshots do you have once the arrow reaches its target?

Can you spot the FINITIST assumption?
THE ARROW REACHES ITS TARGET

If you don't know that the arrow is supposed to reach it's target, then every half division snapshot you make increments towards infinite snapshots.
You take a snapshot, measure how much distance is remaining so you know where half of that is so you can get ready for the moment of the next snapshot, and you do this infinitely. The arrow never reaches its target because every fuckingly small instance of distance is divided in half, leaving another half instance to be covered, ad infinitum. If that means you must zoom in your point of view to differentiate atom distance, you do that. If that means zoom in your point of view to create an arbitrary scale between planck lengths, you do this. The divisions never stop, the snapshots never stop, the arrow never reaches it's target, but under no circumstance is any snapshot identical to another, and since you're too dumb to realize there exists no real/2 = 0, you continue patiently taking snapshots forever.

>> No.9591618

>>9591592
>Oh i see, you were arguing against wolfram the whole time
I'm not arguing against wolfram, I'm arguing that a) you're mixing two different contexts, wolfram being one of them and b) it doesn't matter which context you use if you stick to one.

> You're also an idiot who decided to interject by continuing a reply thread started by someone who wasn't you.
You mean I called you out on your bullshit? Boohoo.

>Every proof provided to you, you act like the problem has changed.
Every alleged proof you've given is either irrelevant, gibberish, false, or a combination thereof.

>I say give the tortoise an infinite head start and you act like its a different problem.
You can change the problem however you want, it still leaves the original one to resolve.

>The finite elements of the achilles paradox are that time continues on after the problem.
What does this mean and how is it relevant?

>That no reference frame of the arrow in flight is distinguishable from another reference frame as zero time has passed, and therefore the arrow hasn't moved.
You haven't explained how motion is defined with respect to this "reference frame," so this is just gibberish.

>By the implement of his infinite division, the arrow never reaches the target, yet he assumes that because the arrow really did reach the target, infinite reference frames of zero motion = motion.
You don't have zero motion, motion is undefined in this "reference frame."

>The truth of it is that he did not actually imagine infinite divisions. If we know the arrow was flung and we know it hit its target, then the flight path can only be finitely divided such thay all divisions summed equal the total flight path, yet Zeno assumes otherwise, or rather tries to imply 0×infinity = 1
The flight path can be infinitely divided, but that doesn't mean your definition of motion will remain coherent. Nothing says that the definition of motion has to remain coherent, thus your argument is based on nothing.

>> No.9591639

>>9591618
Time continuing after achilles reaches the tortoise, assuming infinite divisions were performed along 1/2^n, then means there exist numbers greater than infinity.

Put it this way, for AT = Achilles catches tortoise
Start---------------------AT------------future->
0--------1/2---1/4...--AT------------future->
[math]\frac{1}{2^0}[/math]------[math]\frac{1}{2^1}[/math]----[math]\frac{1}{2^2}[/math]...--AT(n=infinity)---->(future?)
All future n's of reference time after achilles reaches the tortoise come AFTER infinity, meaning INFINITY was SURPASSED.

What the fuck, man. Your brain is literally full of dogshit and broken glass. Like i said, you can't even fucking think and you're just regurgitating retardation uttered by someone else. By the very explicit solution of [math]\sum_{n=1}^{\infty} \frac{1}{2^n}[/math], it assumes NOTHING COMES AFTER 1

>> No.9591643

>>9591639
>Time continuing after achilles reaches the tortoise, assuming infinite divisions were performed along 1/2^n, then means there exist numbers greater than infinity.
Retarded nonsense. 1/2^n does not describe the time after Achilles catches up. If you want to describe it you would have to change the sum to something else.

>> No.9591645
File: 16 KB, 498x467, 1512340128839.png [View same] [iqdb] [saucenao] [google]
9591645

>>9591643
fucking idiot.

You are an absolute fucking idiot. Just shut the fuck up.

>> No.9591647

>>9591639
>All future n's of reference time after achilles reaches the tortoise come AFTER infinity, meaning INFINITY was SURPASSED.
There's just one big problem: n doesn't represent time!

>> No.9591649

>>9591645
>i have no argument

>> No.9591650

>>9591645
So you have no counter-argument and you admit I'm right, thanks.

>> No.9591660

>>9591647
N REPRESENTS A NUMBER
IF YOU REACH INFINITY, IF YOU EVEN CAN (YOU CANT), THEN YOU HAVE REACHED THE END. THERE ARE NO NUMBERS GREATER THAN INFINITY TO COUNT. NO MORE NUMBERS MEANS NO MORE PROGRESS, NO MORE DISTANCE NO MORE TIME. INFINITY = INFINITY.

BELIEVE IN GOD. BELIEVE IN GOD YOU STUPID OF SHIT. YOU AREN'T SMART ENOUGH TO GET BY ON YOUR OWN ACCORD SO BEG FOR GOD'S GRACES.

THESE ARE FUCKING NUMBERS. THEY'RE TRIVIAL. YOU CANT EVEN GET NUMBERS RIGHT ON YOUR OWN. BEG FOR GOD.

>> No.9591670

>>9591660
REEEEEEEEEEEEEEEEEEEEEEEEEE

>> No.9591682

>>9591639
So basically the universe would end once achilles caught the tortoise, and not even zeno would be around to acknowledge the catch ocurred.

>> No.9591687

>>9589173
>this still remains true

>> No.9591735

>>9591639
Kek

Good point. It doesn't mean much that [math]\sum_{n=1}^{\infty} \frac{1}{2^n}[/math] converges to 1 but sums don't converge to infinity, even though the convergence to 1 is this equation is just using 1 as a stand-in for infinity as the largest possible value it could sum to, but unfaithfully not extending the vagueness of infinity to it while treating it like normal real number 1 which everyone counts ahead of 2. Mathleticians are drooling brainlets.

>> No.9592458

>>9591592
Another flaw in your argument is that you are using the uncountable infinity of the extended reals to say that 1/inf = 0, while 0+0+0... = 0 uses countable infinity. One has nothing to do with the other.

>>9591616
>The divisions never stop, the snapshots never stop, the arrow never reaches it's target, but under no circumstance is any snapshot identical to another, and since you're too dumb to realize there exists no real/2 = 0, you continue patiently taking snapshots forever.
You are confusing the number of divisions with the amount of time. The amount of time is finite, so there is a point at which infinite snapshots have been taken, otherwise the photographer did not follow the instructions of the problem. This is because the time between snapshots keeps getting shorter very quickly.

>> No.9592468

>>9591735
>Mathleticians
you can't math or spell.
figures

>> No.9592533

>>9589113
converging to infinity is well defined with basic [math]\epsilon - \delta[/math] formalism, read a book brainlet

>> No.9592573

This is, quite possibly, the most fucking retarded thing on /sci/ currently. How the absolute fuck can you argue about the existence of infinity for over 150 posts. Go find some other god-tier math problem to work on. Not this shit again.

>> No.9592715

>>9592458
That was Zeno's argument. Learn about the topics being discussed ffs.

>> No.9592720
File: 54 KB, 680x380, 17zpe7.jpg [View same] [iqdb] [saucenao] [google]
9592720

>>9592468
Brainlet [math]\rightarrow[/math] Mathlet

>> No.9592756

>>9592573
Whether it exists as a concept is not up for debate. You can't deny God exists by your logic, given religion is already pre-established.
The point is, this "concept" of infinity is not actually rigorously defined with a consistent framework. You should be able to read all the posts here and see how proponents of infinity constantly flip flop on definitions while jumping through hoops. In one moment it's a number, in another it can't be incremented to, in yet another it can be incremented to, in some it is a direction of never ending countability over the reals, in others it can be fully counted and achieved in past tense, and in ALL cases the usage of it by their own provided interpretation can be extended to prove infinity does not have actual accurate mathematical value to arithmetic for extracting real solutions to real problems.

So sure, "infinity" as a word vaguely describing a vague idea exists, but literally no one knows what it means or how to properly use it. People consistently treat the convergence of [math]\sum_{n=1}^{\infty} \frac{9}{10^n}[/math] to mean something intelligible despite the 1 it is converging to being the maximum possible sum it ever could be, which is the analog for infinity as a real number. No one knows what number value infinity as a number has, yet when infinite integers are restricted as decimals between 0 and 1, they treat the 1 it never can properly reach as reachable, and treat the 1 as the normal real countable 1 that comes after 0 and before 2, even though this is a hypothetical 1 that is merely an alternative symbol notation for the vague non-existing number of [math]\infty[/math].
It's pure fucking idiocy. If 0.999... = 1, then any real = infinity, and that is as simple as the claim gets. If you refuse to acknowledge it, you are a brainlet and shouldn't be allowed to teach math.

>> No.9592770

>>9592533
You can't converge to an undefined value. Approaching infinity is known as divergence. It's the opposite.

>> No.9592778

>>9592756
0.999999..... is never 1 anon
there is no such thing as close enough in math

>> No.9592782

>>9587117
>you can't even make it two minutes pondering how big infinity could go counting in increments of a million each second.

120 million

Wtf I'm a genius now

>> No.9592785

>>9592715
No, Xeno's argument says nothing about in infinities or dividing anything up. It simply illustrates that motion is undefined in a "moment of time."

>> No.9592795
File: 3 KB, 280x272, cGIay9e.png [View same] [iqdb] [saucenao] [google]
9592795

>>9592785
>In the arrow paradox (also known as the fletcher's paradox), Zeno states that for motion to occur, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that in any one (duration-less) instant of time, the arrow is neither moving to where it is, nor to where it is not.[13] It cannot move to where it is not, because no time elapses for it to move there; it cannot move to where it is, because it is already there. In other words, at every instant of time there is no motion occurring. If everything is motionless at every instant, and time is entirely composed of instants, then motion is impossible.

>> No.9592812

>>9592756
>mathematical logic
>set theory
>order theory
>the theory of metric spaces
>real analysis

you've never heard about any of these, have you

>> No.9592813

>>9589244
>1/9 > 0.111...
what if you multiply 1/9 by 9?

>> No.9592820

>>9592812
>moving the goal posts
you've never heard about this have you.

>> No.9592822

>>9592813
I dunno man you fuckin' tell me. What happens when you multiply [math]\frac{1}{9} × 9[/math]?

>> No.9592828
File: 78 KB, 1300x863, 10471559-Puzzled-man-at-computer-shrugs-shoulders-and-expresses-lack-of-knowledge-Stock-Photo.jpg [View same] [iqdb] [saucenao] [google]
9592828

>>9592822

>> No.9592837

>>9592756
Your first mistake is thinking that infinity is a number with a clearly defined value. Please try again.

>> No.9592844

>>9592756
>constantly flip flop on definitions
If you've actually been reading, you should know that it's pretty consistent that you can't use infinity outside of limits, summations and sets.

>> No.9592847

>>9592837
How is that my mistake?
Here are part of the post you just responded to which you didn't read:
>"infinity" as a word vaguely describing a vague idea exists, but literally no one knows what it means or how to properly use it.
>this "concept" of infinity is not actually rigorously defined with a consistent framework.

So how is it my mistake and not yours in thinking I believe infinity is clearly defined when I quite literally obviously just claimed it wasn't?

>> No.9592850
File: 29 KB, 640x432, fb0.jpg [View same] [iqdb] [saucenao] [google]
9592850

>>9592844
[math]\frac{1}{\infty} \\ 0.\bar{3}[/math]

Guess we'll just ignore these, right?

>> No.9592858

>>9592850
Both of which still relate to the concept of a limit, you fucking retard. Riddle me this, how would you arrive at [math]\frac{1}{\infty} \\ 0.\bar{3}[/math] using only standard arithmetic and without using limits in the first place?

>> No.9592859

>>9592756
>Whether it exists as a concept is not up for debate. You can't deny God exists by your logic, given religion is already pre-established.
Whether something exists in mathematics is to say that it's a consistent construct resulting from accepted axioms. This is obviously true for infinity, which has been conceptually constructed over hundreds of years by mathematicians much much much smarter than you. Whether god exists on the other hand is an empirical question.

>The point is, this "concept" of infinity is not actually rigorously defined with a consistent framework. You should be able to read all the posts here and see how proponents of infinity constantly flip flop on definitions while jumping through hoops. In one moment it's a number, in another it can't be incremented to, in yet another it can be incremented to, in some it is a direction of never ending countability over the reals, in others it can be fully counted and achieved in past tense,
This point rests solely on your ignorance of the concept you are trying to criticize, your inability to distinguish between different contexts and your conflation of them. All of your arguments have been shown to be flawed. Point to one that hasn't.

>but literally no one knows what it means or how to properly use it.
Stop projecting.

>No one knows what number value infinity as a number has
Wrong. Aleph-null is the number of natural numbers, aleph-one is the number of countable ordinal numbers, etc.

>If 0.999... = 1, then any real = infinity
Wrong by definition.

>> No.9592865

>>9592847
>rigorous proof
The only definition that most people will only ever encounter is "unbounded limit" and has been pretty fucking consistent over-all. My calculus wouldn't work otherwise.

>> No.9592867
File: 44 KB, 526x939, Screenshot_2018-02-23-21-20-34-1.png [View same] [iqdb] [saucenao] [google]
9592867

>>9592858
I dunno nigger. Maybe by not using limits and actually knowing how to at least do 3rd grade math.

If you cant understand that 1/n becomes a smaller and smaller result as n increases as a number, and can't make the assuming leap that if such a greatest number were to exist as infinity, the result of 1/infinity would be the closer to zero than any real number n. You dont need limits to do fucking toddler math.

>> No.9592877

>>9592867
>If you cant understand that 1/n becomes a smaller and smaller result as n increases as a number
You're literally using limits if you're saying that, you're just avoiding the use of the [eqn]lim_{x \to ∞}[/eqn]. It's like saying you don't need algebra to do some trigonometry and then immediately proceeding to a ten paragraph problem that starts with "Suppose there is a number..."

>> No.9592878

>>9592859
Argue with yourself, i'm done. You're too stupid to learn much less think and follow proofs and it's easy to see why when you adamantly believe in a stupid concept like infinity. You are blindly referencing axioms and theories and blindly assuming intelligence gaps. You must be blindly doing it since you can't understand a proof in the first place. You are a literal actual idiot and no one wants to be like you or think like you or act like you. Much of your arguements throught the thread have literally just been saying "Wrong" but not providing anything to accomodate the accusation. Proof is provided to you and you hust shake your head and scream like an autistic child. "NONONO ITS NOT TRUE I DONT BELIEVE IT" this is literally (You).

Post porn so you can earn a ban.

>> No.9592880

>>9592795
So you agree that Xeno's argument says nothing about infinities or dividing anything up, thanks.

>> No.9592881

>>9592880
He's dividing time into "instants".

>> No.9592882

>>9592877
No, i'm just doing a division. I'm not using a limit. If i start using a limit, you'll start bringing up irrelevant axioms attributed to the hard defined methodology of limit. Moving the goal posts. If you think sequential math didn't exist before limits, you are an idiot.

>> No.9592890

>>9592867
So 1/3 = 0.333...

Thanks for admitting 1 = 0.999...

>> No.9592893

>>9592882
>I'm not using a limit
Then explain
>1/n becomes a smaller and smaller result as n increases as a number
Because that's how you literally translate [math]lim_{x \to ∞} \frac{1}{n} = 0[/math].

>> No.9592900

>>9592878
>Argue with yourself, i'm done.
So you admit I'm right since you can't even come up with an argument. Thanks.

>Much of your arguements throught the thread have literally just been saying "Wrong" but not providing anything to accomodate the accusation.
That which can be asserted without evidence can be dismissed without evidence.

>Proof is provided to you
No actual proof had been provided since your alleged proofs all have fatal flaws. If you disagree, I suggest you respond to these flaws. If you don't then no one had any reason to believe the proofs are true. It's solely your own fault.

>> No.9592902

>>9592881
Where does it say anything about dividing?

>> No.9592906

>>9592902
>In any one (duration-less instant of time)
>at every instant of time
>and time is entirely composed of instants

>> No.9592907

>>9592858
Okay you know what. Lets just pretend for a moment you were right.
So tell me the similarities between the following since you claim infinity is consistently defined
[math]A: \lim_{n \rightarrow \infty} 1-2^{-n} \\ B: \sum_{n=1}^{\infty} \frac{1}{2^n}
\\ C: 0.\bar{9} \\ D: \frac{\mathbb{R}}{\infty} = 0[/math]

One singular definition of infinity needs to apply to all 4 examples consistently. Provide it.

>> No.9592911

>>9592890
1/3 > 0.333...
Thanks for being retarded and assuming I said something I hadn't.

>> No.9592919

>>9592907
"unbounded limit" or "arbitrarily large" should cut it.

>> No.9592937

>>9592919
Then that means
[math]\lim_{n \rightarrow \infty} 1-2^n < 1 \\
\sum_{n=1}^{\infty} \frac{1}{2^n} < 1 \\
\0.\bar{9} < 1 \\ \frac{\mathbb{R}}{\infty} = \text{undefined}[/math]

>> No.9592944

>>9592900
tits or GTFO

>> No.9592945

>>9592937
That is only correct if you actually choose to end your infinity somewhere. It's meant to be infinity, it's not meant to end. Try again.

>> No.9592953

>>9592945
No, its correct because it never reaches the end.
Increment 0.0 to 1 by 1/5

0.2 < 1
0.4 < 1
0.6 < 1
0.8 < 1
1.0 = 1

Its only equal if the end occurs. It doesn't occur in infinity. I asked a single consistent definition of infinity, i didn't also ask that you arbitrarily try to redefine basic logic to accomodate it.

>> No.9592956
File: 150 KB, 979x832, 8d87e0_6355017.jpg [View same] [iqdb] [saucenao] [google]
9592956

If the sum of 1 to infinity is -1/12
than the sum of 2 to infinity is -13/12

>> No.9592964

>>9592906
So no dividing, thanks.

>> No.9592967

>>9592919
>>9592953
Also by the way, "arbitrarily large" and "unbounded limit" don't mean the same thing, so you screwed up right there in the first place. 10^290653 is arbitrarily large. Never reaching an end is unbounded. One definition, pick it.

>> No.9592970

>>9592911
Your picture says 1/3 = 0.333...

>1/3 > 0.333...
So what real number is between them?

>> No.9592974
File: 38 KB, 645x729, 1509035922690.png [View same] [iqdb] [saucenao] [google]
9592974

>>9592964

>> No.9592976

>>9592937
Only the fourth follows.

>> No.9592983

>>9592953
>It's only equal if the end occurs
That's where you start disagreeing with standard mathematics. It's not me that "redefined basic logic", it's you. You've essentially declared a value to something that is supposed to be infinity. [math]lim_{n \to \infty} 1-2^n < 1[/math], for example, is only true if you actually ended it somewhere and if you actually ended it somewhere, it's no longer infinity. You have, essentially, declared a boundary, which goes against the very definition of infinity.
>>9592967
If you're going to be absolutely pedantic about it, then sure, let's go with "unbounded" or "without bounds".

>> No.9592985
File: 37 KB, 340x565, 1514683747604.jpg [View same] [iqdb] [saucenao] [google]
9592985

>>9592970
The picture is depicting how to perform the first few steps of long division you mongreloid. There is no equation assignment "equal sign" operator present.

>> No.9592992

>>9592983
Jesus you are fuckung stupid and desperately trying to redefine logic as well as your own provided definition.
You define infinity as unbounded, aka unending.
Sum 1/5 is less than 1 until the end has been reached
0.2 < 1
0.4 < 1
0.6 < 1
0.8 < 1
1.0 = 1

So given you can't reach the end of infinity, because you defined it as unending, you can't reach the equal sign and instead only have values less than 1 for the 4 examples.

>> No.9592996

>>9586648
>sums by definition are finite

>> No.9593005

>>9592992
>>9592983
Please tell me you understand what just happened here and why it makes infinity poorly defineable and easily breakable.

>> No.9593006

>>9592992
Ever heard of the concept of "convergence"? If you allow a convergent series to go on infinitely, it will reach its limit, likewise, if you cut it somewhere it will always stop short. Key here is that it has to be unending. It's your fault if you have to insist that operations of infinite sequences and other similar behavior need to have an "end" and reach the equal sign.

>> No.9593007

>>9593005
"without bounds" seems like a pretty solid definition to me. You're operating under the assumption that an infinite series needs to have an end, contradicting the definition of "infinite" in the first place.

>> No.9593026

>>9593006
Okay so i guess you dont understand..

You would be right to assume I cutoff and ended prior to infinity if I claimed that A or B were equal to a single, specific, finite number smaller than 1. But that's not what I'm saying. I'm saying that the value is less than 1 and not equal to anything specifically, which is true because you've defined infinity as unending and without an end there can be no final equivalence. More than just unending, every instance of endable finitivity that occurs within the incrementing n provides that all of these values are less than 1, and that there exists no next value that isn't also less than 1, and this continues unending.

So given the claim that the results of A and B must be less than 1, but also that if the results of A and B were any exactly finite value less than 1 they would have ended before infinity, you should bow have enough information to understand that one assumption is false and that assumption is "infinity makes sense".

There you go. Infinity doesnt make sense. You cant use it without invoking idiocy and paradoxes, so the only winning answer is to simply refuse to use it in arithmetic at all.

>> No.9593044

>>9593006

>>9592770

>> No.9593088

>>9593026
>without an end there can be no final equivalence.
Again, that is your assumption, not mine. Your case is that you need some sort of "endability" which is where this entire retardation stems from.
>if the results of A and B were any exactly finite value less than 1 they would have ended before infinity
That's your retarded assumption. It's supposed to end AT infinity, not along it.
The reason why a convergent series is equal to something is because for every quantity less than the limit of an infinite convergent series, there will always be a number greater than that. However, there will never be any number greater than its limit, therefore the limit is the definition of that particular infinite convergent series.
[eqn]lim_{x \to \infty} 1-x^{-2} = r[/eqn]
You need to define where this r is. If you're going to define it anywhere less than 1, there is a guaranteed quantity greater than it that still within its bounds. There will never be a qunatity, however, that is greater than 1, so this is where the limit is defined at.

>> No.9593107

>>9593088
You defined infinity as unbounded, unending. You can't reach infinity. You can't arrive AT infinity. If you arrived AT infinity, you would have an end, and you can't arbitrarily redefine the act of doing something as doing it infinitely before you've finished doing it.

You are literally trying to arbitrarily redefine logic itself to accomodate your shitty definition for an already shit concept. You are insane dude.

>> No.9593196

I have a 20lb bag of potatoes. Potatoes come in different shapes and size cause thats just how potatoes are, so there is no indicilation of the exact quanitity of individual potatoes in the bag, just that they collectively weigh 20lbs and they are different sizes. I want to know the exact quanitity of individual potatoes in the bag, so i open the bag and pull potatoes out one by one to count them individually.

The moment i count the first potato, I am not then infinitely counting potatos for the remainder duration of counting the potatoes in the bag. I am simply just counting potatoes. I end up counting 26 potatoes and have finished what i set out to do. At no point during or after the act of counting potatoes was I doing it "infinitely".

Imagine you're a potato farmer. Your life is counting potatoes, but not really. You've been sorting potatoes into bags for years and you couldn't put an exact number on how many bags of potatoes you've harvested if you tried. There is probably a written record of it somewhere for business purposes, but its not off the top of your head. You love farming potatoes and would gladly do it forever god-willing you were immortal, so the god of potatoes grants you immortality to make your wish come true. You may now infinitely farm potatoes. At no point during history will you have ever harvest or sold an infinite amount of potatoes, however. It will always have been a finite number of potatoes, even though you're doing it infinitely without end.

>> No.9593457

>>9593107
>argument only consists of vague referemces to "redefining logic"
If that's your best argument then you're as good as lost. Provide a counter example. Provide a definite value that would define the limit at a value less than the limit. I guess using the word "AT" is way too much to process for a brainlet like you. Let me rephrase that. If you allow the operation to proceed infinitely, the operation is going to tend towards value. You're so fucking stupid that useless pedantry seems to be your only argument.

>> No.9593460

>>9593196
numbers are not physical object

>> No.9593475

>>9592985
Then do tell me what number is between 1/3 and 0.333...

>> No.9593484

>>9593475
Considering you cant have an infinite amount of something, the 3's in 0.333... are not infinite and instead arbitrarily finite, at which a number with one more 3 in the very least exists, and one more after that, and more again, infinitely, such that the arbitrary number of 3's which you initially invoked are in fact infinitely far away from having an infinite amount of 3's.

>>9593457
You are forsaken.

>> No.9593488
File: 815 KB, 194x146, ArtisticNeglectedHare-max-1mb.gif [View same] [iqdb] [saucenao] [google]
9593488

>>9593026

>> No.9593573

>>9592937
for the first 2
there is a preservation of weak inequalities, but no similar result for strong ones. This means that these need to be weak inequalities not strong ones
<= rather than <

>> No.9593634

>>9593573
It is a strong inequality given you cant have any equality because you never reach a final summation because infinity has no ending. The only valid operator you can use in the situation is "less than". What you know of the partial sum problem is that for every n, the total of partials is definitely less than 1, and without an end to summation there can be no final n of finite equality.
1. You can only assume <
2. You can't have an =

Therefore, the solution to the problem without knowing what it ought to be is undefined, but knowing that the maximum possible value of the solution is a hypothetical 1 that is analogous to infinity, thusly allows you to solve the sum of the equation is definitely less than 1, and definitely not anything else than "definitely less than 1", for if 1 were to be achieved, so then must infinity as a number on the numberline after a definite real number also be achieved.

Infinity fags are the real finitists. Before infinity fags, everyone was well off enough just believing bigger numbers can exist, and didn't have problems dealing with definite decimal accuracy. Infinity fags with their mental retardation couldn't grasp that ideology however, and instead insisted a largest number must exist, and it must be infinity, and that you can't increment past infinity cause it is the biggest of which there are no bigger.

Infinity fags are brainlets who can't imagine arbitrarily large numbers so they concatenate the effort and leave it up to personal interpretation. A smart person will think infinity is larger than sone insanely unecessarily large number, but infinity fags will basically treat it as 10 but just keep their mouthes shut so they can pretend to feel smart when a much smarter person describes it.

Eat shit. Flush infinity down the toilet.

>> No.9593811

>>9593196
So what?

>> No.9593817

>>9593484
>Considering you cant have an infinite amount of something, the 3's in 0.333...
There are an infinite amount of 3s in 0.333... Try again.

>> No.9593823

>>9593634
>It is a strong inequality given you cant have any equality because you never reach a final summation because infinity has no ending.
You immediately reach the sum because the process for calculating it does not even involve infinite operations.

>> No.9593852
File: 5 KB, 211x239, 1509035948911.jpg [View same] [iqdb] [saucenao] [google]
9593852

>>9593823
This is (you) right now
>1 = infinity!

>> No.9593887

>>9593823
Do you assume repeating decimals didnt exist before calculators?
Do you assume all calculators in history have "instantly" printed a result?
Do you know how to perform long division?
Do you instantly get zero point infinite 3's when performing long division on 1/3?

Do you have anything of actual value to offer mankind or is it just /sci/ you shitpost on.

>> No.9593901

>>9593887
>Do you assume repeating decimals didnt exist before calculators?
No.

>Do you assume all calculators in history have "instantly" printed a result?
If by instantly you mean that they have printed a result after a negligible amount of operations, no.

>Do you know how to perform long division?
Yes.

>Do you instantly get zero point infinite 3's when performing long division on 1/3?
It only takes a few operations to reach the infinite loop, at which point you know that there are infinite 3s. Your contention that there aren't infinite 3s is just objectively wrong.

>Do you have anything of actual value to offer mankind or is it just /sci/ you shitpost on.
Math involving infinity - basically everything after and including the construction of the reals - is of immense value to mankind. You're shitposting on the other hand has zero value.

>> No.9593954

>>9593901
Present 1(one) example where a real world problem requires [math]\infty[/math] to solve it.

Everything else you said is wrong else you wouldn't have been stupid enough to say it in the post prior. Of course you believe writing two or three 3's means you have written infinite threes instantly. Not the point though.

Present one real world application that you believe requires infinity to solve a problem.

>> No.9594010

This is the worst thread I have seen here in a while.

>> No.9594022

>>9593954

Whether it's "practical" is completely irrelevant.

>> No.9594050
File: 232 KB, 300x300, 1307889832001.png [View same] [iqdb] [saucenao] [google]
9594050

>>9594022
>Math involving infinity - basically everything after and including the construction of the reals - is of immense value to mankind.
Present
the
value

>> No.9594056

>>9594050

I just said it doesn't matter if it's practical. I couldn't care less if you think infinity isn't practical outside of mathematics.

>> No.9594060

>>9594056
And literally no one could care less about the made up fantasy bullshit inside your imagination.

>> No.9594065

>>9594060

Which is?

>> No.9594145

What is [math]\frac{9}{10}[/math]th's of infinity?

What is [math]\frac{9}{10} + \frac{9}{100}[/math] of infinity?

What good are convergence and divergence when they both describe the same thing? And since they are both the same thing, why is convergence attributed to equivalence while divergence is attributed to uncertainty?

I can't honestly be the first one to judge how useless this all is. Has everyone just been sitting around with their thumbs up their asses taking infinity and limits and calculus as granted defacto information worth learning, much less all the related math fields which implement infinity in one way or another.

One of the basic fundamentals of math is figuring out how to accomplish a task in a different, often faster way, and it's called simplifying. The videogame doom from 1993 would not have been possible if the lead programmer didn't have a good understanding of math, cause it was from simplifying expensive to compute math like sin, arc, tan, and cos which allowed the visual depiction of a 3D world without three dimensional matrices and polygons.

Infinity on the other hand seems to be something going in the opposite direction from simplification; being overcomplication, redundancy, and arbitrary needlessness.
Much of the most important inventions throughout history have come from simplifying complex actions. Firearms made war and hunting more simple and faster. Vehicles made travel more simple and faster. Telecommunications made communicating more simple and faster. So what is this arbitrary backwards thinking of wanting to overcomplicate by feeling infinity is somehow necessary? It is essentialy anti-existence to strive for chaos rather than order.

>> No.9594179

>>9593484
>You are forsaken.
When are you going to have an argument other than "y-you're just illogical". I presented my case and you have to do better than just shout "YOU'RE ILLOGICAL YOU'RE ILLOGICAL YOU'RE ILLOGICAL" over and over agian.

>> No.9594191

>>9593954
Have you ever taken a calculus course? The very foundation of calculus is based on infinite limits.

>> No.9594200

>>9594179
Your "argument" was literally strawmanning me. That isn't an argument, its a logical fallacy, and doing this insults me so it's also ad hominem. You are forsaken. You can't present a good argument. I can't take you seriously. At least in the posts I've called you every name under the sun i also included maths and logics, meanwhile you just end at the ad hominem and move on and keep trying to derail back to shitflinging.

You were attempting to talk about convergence, were you not?
That means you didn't read the other posts about how convergence is not dissimilar from divergence. Divergence is a value tending towards infinity, yet 1/2^n merely shifts the work from incrementing integerally between 0 and infinity to incrementing decimally between 0.5 and 1, ans this means the 1 in this situation is a direct analog to infinity in totality. You aren't "converging" to 1, you're just starting at a value that is arbatrarily closer to infinity than 0. What is infinity divided by 2? Doesn't compute. What is 1 divided by 2? Oh! It's 0.5!
You are treating the 1 value that it could maximally possibly be as the real number one instead of the vague analog of infinity, and consider this converging to 1, when in reality it is just diverging towards infinity.

>> No.9594218

>>9593954
>Present 1(one) example where a real world problem requires ∞∞ to solve it.
Real world problems often require the real numbers, limits, calculus, etc. All of modern physics is based on this. All of these require the use of infinity. Further, the standard cosmological model is that the universe is infinite, since it's flat and spacial boundaries don't make much sense (this also assumes that space is simply connected, which is the simplest assumption).

>Of course you believe writing two or three 3's means you have written infinite threes instantly.
What does "written" have to do with whether 0.333... has infinite threes? What a pathetic attempt to move the goalposts.

>> No.9594234
File: 43 KB, 1366x623, geometric convergence.png [View same] [iqdb] [saucenao] [google]
9594234

>>9594200
>You are treating the 1 value that it could maximally possibly be as the real number one instead of the vague analog of infinity, and consider this converging to 1, when in reality it is just diverging towards infinity.
What the fuck would you call pic related then? The reason it converges is because it tends towards that one value. There will never be any condition where it reaches beyond that value for any value declared by "cutting" a sequence somewhere, there will always be another value bigger than it but is still below the value that it converges to. It's only logical that if you were to allow a sequence to approach infinity in the domain, the range will never reach beyond +1. Divergence means that it does not tend to anything, it will reach all possible values in the range.

>> No.9594240

>>9594145
>What is 9/10th's of infinity?
Which infinity?

>What good are convergence and divergence when they both describe the same thing?
They don't.

>Infinity on the other hand seems to be something going in the opposite direction from simplification; being overcomplication, redundancy, and arbitrary needlessness.
So is all of math. You're absolutely right, we should only try to simplify math. We should just go back to counting on our fingers. Toes would just complicate things. No wait, one finger would be even simpler. Behold the apotheosis of mathematics: counting one finger. We did it reddit!

>> No.9594271

>>9594240
>Peano Axioms

>> No.9594286

>>9588246
this is the answer

>> No.9594323

>>9594271
>Peano Axioms
Too complicated, that creates an infinite set of natural numbers. Only one number exists, that is the true mathematics.

>> No.9594330

>>9587117
>Infinity doesn't need to exist in math

well then calculus wouldn't work, dipshit

>> No.9594337

>>9589154
Imagine being both this confident and this retarded. Must be a business major.

>> No.9594341

>>9594337
Worse, I bet he's a "software engineer."

>> No.9594367

>>9594240
Ironically you can can count over a thousand with finger binary and only ten with finger decimal. Unfortunately, counting by tens makes more sense than thousands, at least made more sense for the better part of the history of mankind.
Really, all you have is strawman. It's shit, buddy. I bet you're a real piece of garbage.

>>9594234
You can't converge to infinity. It's not a k own value. Just expand upon your very image requiring the number line on the x axis to show convergence. Now place infinity on the numberline and converge to it.
(Protip: you can't sensibly do this)

You and mathleticians at large seem to be mistaking convergence to a finite result via an infinite sum or limit as being necessary or truthful. In reality, once again, all you're doing is mapping 0 to infinity(an unknown value not on the numberline) to a different set of definitely finite values like 0 and 1. You are confusing the fact of the mapping from unknowable to presumptiously knowable by ignoring that 1 represents infinity, for example your graph is a fallacy. Nothing occurs after x=1, yet the graph continues on towards 7. At x=1, this is the analog for infinity and nothing can come after infinity.

You're misunderstanding a definite and FINITE granted fact that arbitrary decimal accuracy is not required for any real world application for a defacto reason that a decimal getting smaller and smaller is equivalent to each [math]10^{-n}[/math] becoming more and more insignificant towards real usage. So because all real usage of decimal extension is to a finite amount of places and not an infinite amount, you presume that surpassing an average understanding of what is acceptably smallest must then simply equivocate towards convergence and therefore equality. ->

>> No.9594370

>>9594367
This is where the general fuckup occurs away from truthful precision towards ambiguity. Converging to 1 is meaningless when 1 is just a stand-in for infinity, because infinity is meaningless as a value beyond simply knowing it's unreachable which should more than well provide the information necessary to see that approaching 1 from 0.999••• as the analog for infinity is also unreachable. Failing to understand this is literally swapping the definition of infinity for convenience, which only goes towards providing evidence for how infinity is misunderstood and misused.


>>9594330
Calculus isn't necessary to accomplish anything.

>> No.9594393

>>9594286
Aleph requires infinity be well defined. Aleph is truthfully a misnomer and attempt at shifting the problems of infinity onto a different element as a means of deceit.

>> No.9594405

>>9594367
My mistake i didnt even read the equation
Just subsititute that paragraph with assuming [math]1-x^{-n}[/math]

>> No.9594449

>>9589304
fuck off with your [math] 9_{ \frac{monkey}{banana}} [/math] bullshit

>> No.9594460
File: 224 KB, 481x325, 1518634307153.png [View same] [iqdb] [saucenao] [google]
9594460

>>9594449
Fuck off with your ad hominem and strawmans you insignificant piece of shit.

>> No.9594563

>>9594370
>infinity is meaningless as a value
No it's not. See the one point compactification of the complex plane or rather, the projective plane. Meromorphic functions are suddenly holomorphic functions and your favourite complex analysis theorems extend to this space. Why would we care about meromorphic functions? Well the Residue theorem for one, which in particular gives us a method of computing inverse Fourier transforms on real valued functions.

Not sure what you're trying to say after that. It appears fairly confused to me. I have a feeling though of what you might be talking about. If you're going to talk about 0.999... , then it seems to me you are talking about some kind of sequence of numbers, namely, the sequence (0.999... n)_n as n becomes large. If you take a sequence and find a number in which this sequence is arbitrarily getting closer to this number, then this number is defined to be the limit of this sequence. Limits are (obviously) unique. Since 0.999...n gets arbitrarily close to 1, 1 is its limit and since 0.999.... is by definition the limit of this sequence, we must have 1 = 0.999....

>> No.9594575

>>9594145
So you're saying we shouldn't try to understand infinity because it's too hard?

>> No.9594577

>>9594563
Thanks for the opportunity to provide an example of simplifying a complicated process to make it faster

https://en.m.wikipedia.org/wiki/Fast_Fourier_transform

Infinite elements removed and renderee unecessary.

>> No.9594584

>>9594563
The repeating decimal in 0.999... doesnt get closer to 1, it only gets closer to an arbitrary cutoff limit of decimal value. This was detailed here:
>>9594367
>You're misunderstanding a definite and FINITE granted fact that arbitrary decimal accuracy is not required for any real world application for a defacto reason that a decimal getting smaller and smaller is equivalent to each 10−n10−n becoming more and more insignificant towards real usage. So because all real usage of decimal extension is to a finite amount of places and not an infinite amount, you presume that surpassing an average understanding of what is acceptably smallest must then simply equivocate towards convergence and therefore equality.

0.999... will instead always be infinitely far away from 1, just as any real is equally infinitely far away from infinity.

>> No.9594596

>>9594577
What's your point?

>> No.9594600

>>9594584
Wrong.

https://www.wolframalpha.com/input/?i=0.999......

>> No.9594605

>>9594584
>0.999... will instead always be infinitely far away from 1, just as any real is equally infinitely far away from infinity.

No.
|1- 0.9| = 0.1
|1-0.99| = 0.01
|1- 0.999 = 0.001,...
|1-0.9...9| (n 9's) = 0.0...01 (8 0's)

The sequence is indeed getting closer to 1. You take any real number epsilon and choose n so that 0.9...9 (with n 9's) is smaller than epsilon away from from 1. Just by definition this sequence converges to 1.

>> No.9594612
File: 12 KB, 478x523, pic_related_its_you.png [View same] [iqdb] [saucenao] [google]
9594612

>>9594584
>0.999... will always be infinitely far away from 1
It's between 0 and 1 so it can't be any farther than 1 away.

>> No.9594628

>>9594605
[math]\frac{9}{10}[/math] of infinity is less than [math]\frac{9}{10} + \frac{9}{100}[/math] of infinity is less than [math]\frac{9}{10} + \frac{9}{100} + \frac{9}{1000}[/math] of infinity, yet none of this puts you any closer to infinity than 0 would. Its false equivalence. If you assume to reach 1 from 0.999..., you equally assume to reach infinity from the reals, or rather that infinity is a real number.

If you can't understanding mapping and analagous values, or that increasing insignificance over continually arbitrary decimals beyond acceptable, then i dont know how to help you or have a discussion with you. You clearly don't know nearly enough about mathematics as you claim, which porbably extends from a lack of any computer science or engineering knowledge. Whether it interests you and you agree with it or not is irrelevant to the fact computer aided calculation is a logical extension and expansion beyond bullshit unreal fantasy maneuvers performed on figuratively imaginary values and results.

>> No.9594631

>>9594612
There will always be unending decimals. The fact the decimals never ends means it never reaches infinity, and never accomplishing something is as good as not at all. Its infinitely far you mongoloid.

>> No.9594661 [DELETED] 

>>9594628
The likelhood that anyone who visits sci uses computer aided calculation that has true arbitrary accuracy or doesn't treat infinity as a literal real number value greater than [math]2^{1024}[/math]
If they use a calculator that is already designed to give them the answer they've been taught(misled), they will feel vindicated in arguing. The dont understand the computer but use it anyway.

>> No.9594667

>>9594628
The likelhood that anyone who visits sci uses computer aided calculation that has true arbitrary accuracy or doesn't treat infinity as a literal real number value greater than [math]2^{1024}[/math] is slim.
If they use a calculator that is already designed to give them the answer they've been taught(misled) to believe, they will feel vindicated in arguing. They don't understand the computer but use it anyway.

>> No.9594669

>>9594628
>9/10 of infinity is less than 9/10+9/100 of infinity is less than 9/10+9/100+9/1000 of infinity

What does this even mean? What do you mean "of infinity"?

>yet none of this puts you any closer to infinity than 0 would

What does THAT even mean?

>If you assume to each 1 from 0.999...
The only assumption is what I've assumed you mean by 0.99..., which I assume you mean to be the limit of the sequence (1/9 + ... + 1/9^n)_n. As I said above, 1 is also a limit of this sequence. If sequences are what you don't believe in, then I don't know what to tell you. I'm a mathematician and don't care whether or not the concepts I'm dealing with philosophically bear resemblance of real world objects or not.

>> No.9594673

>>9594669
Woops should've wrote (1/9 + .... + 9*10^{-n})_n not (1/9 + ... + 1/9^n)_n.

>> No.9594679

>>9594669
If you truly didn't care, you would argue that arbitrary infinite decimal expansion of 0.999... truly does seperate it from 1.

But instead you argue for convergence and pretend it is different from divergence.

>> No.9594684

>>9594628
>Whether it interests you and you agree with it or not is irrelevant to the fact computer aided calculation is a logical extension

I completely disagree with you. The reason you can use computers to do real world computations such as approximating pi for example, depends on the fact the real numbers are complete (sequences that look like they should converge indeed converge) and various other analysis facts. For example, pi is literally a number which has an infinite decimal expansions, so using methods to approximate it will bear resemblance to something akin to approximating 1 with sequences of 0.99...9.

>> No.9594688

>>9594679
>arbitrary infinite decimal expansion of 0.999...
What?

So that we're on the same page, what do you even define 0.999... to be?

>> No.9594698

>>9594684
Pi doesnt converge, nor does it end. If you say it is infinite expansion, yet accept that pi is a unique number, that being wrong on the 20,000th decimal place is in fact wrong, then you should agree that being wrong on any decimal place would invoke wrongess. If pi is a unique number accepted for its unending expansion, you then do a disservice by not also extending that identity to 0.999••• which even moreso than pi can be any number of real unique numbers [math]\lim_{n \rightarrow } 1-2^{-n}[/math], where the single most obvious identity is 0.333•••×3 derived from the more than obvious fact that [math]\frac{1}{3} > 0.\bar{3}[/math]

>> No.9594702

>>9594679
Actually, I have more questions. Do you believe that convergence is an invalid concept altogether? Like I said, in this case, you are free to think pure math is useless, as it might appear, but then there's nothing to debate as I'm not having a philosophical debate. Are you trying to say 0.999... is somehow equal to infinity? Or are you saying 0.999... diverges but not to infinity, and so perhaps diverges in the same sense ((-1)^n)_n diverges or are you saying R is just not complete (that only rational numbers exist, much like Wildeberger). The latter involves another philosophical debate I won't have.

>> No.9594717

>>9594698
>Pi doesnt converge, nor does it end.
What do you mean by convergence? Pi is a number, the concept of convergence here is meaningless.

>extending that identity to 0.999••• which even moreso than pi can be any number of real unique numbers limn→1−2−n

You're saying 0.99... can be any of the real numbers 1-2^{-n}?????

> 1/3 > 0.3...

I'm beginning to think I'm just being trolled hard. Your choice of confusing wording and explicitly nonsensical definitions is a bit too far for me. If not, I apologize for condescending you.

>> No.9594720

>>9586648
Aleph null I guess?

>> No.9594730

>>9594702
Take [math]\sum_{n=1}^{\infty} \frac{9}{10^n}[/math].
You would say this converges to 1. You say this knowing 1 is the absolute maximum value it could possibly be, even though it doesn't properly reach it. Now take [math]\sum_{n=1}^{\infty} \frac{1}{n}[/math], and you would say this diverges because it approaches infinity. You attribute convergence with equality and divergence with uncertainty, convergence on the positive and divergence on the negatory.

All you've done in the 9/10^n sum is map all possible integers between 1 and infinity to between 0 and 1, then started at 9/10ths the way into the range. This is equivalent to remapping back between 1 and infinity and starting 9/10ths the way into the range, which is as expected undefinable because the numerical value of infinity on a number line is undefinable.
You would presume that any arbitrary incrementing on the non-value of 9/10ths of infinity would then "converge" to infinity, even though approaching infinity is called divergence for the simple fact it cannot get close to any knowable value.

The mapping analogy process between 1 and infinity to between 0 and 1 therefore lends itself to a divine and complete mosunderstanding that the 1 mentioned here is a strict analog of infinity and cannot be reached. You dont converge on 1 any more than you converge on infinity.

>> No.9594744

>>9594717
It can be any real arbitrarily large n, so not really all n. Any arbitrarily large n allows that a significant amount of repeating 9's would arise whereby there is a significant amount of missing information in just "0.999•••" where random non-9 decimals would be present for any [math]\frac{x}{(x+1)}[/math] other than [math]\frac{\bar{9}}{1 \bar{0}}[/math], as shown by taking an infinite sum for this equation to any arbitrarily large n.

>> No.9594746

>>9594744
[math]\frac{x}{(x+1)^n}[/math]

>> No.9594750

>>9594744
Also not really infinite sum, meant to say sigma sum

>> No.9594751

>>9594730
What do you define convergence to be? Sequences are literally mappings between the natural numbers and the real number line and convergence is literally defined to be the value of the function you get as n goes to infinity.

>You dont converge on 1 any more than you converge on infinity.

This is a great observation but the definition of divergence is not what you think it is. The only reason sequences don't converge to infinity is because infinity is not defined to be a real number. Sequences which diverge in this way do so because they are going to a number which is not a real number. It is perfectly valid to work on the extended real numbers which includes infinity as a number. Then I would say 1 + 1/2 + 1/3 +... converges to infinity.

>> No.9594758

>>9594744
>It can be any real arbitrarily large n
Why are you talking about n all of a sudden?

>> No.9594771

>>9594751
The 1 from 9/10^n is also not a real number. Yes, it looks like the number "1", the real number 1 that comes after zero and before 2, but it isn't. Its an infinite limit. It is a literal stand-in analogy for the "number" [math]\infty[/math]. The truthful way to plot 9/10^n is not on a numberline 0 to 1 to 2 to 3 to etc (never reaching "[math]\infty [/math] "), so on and so on. The truthful plot is starting at 0 and creating an arbitrary scale of decimals that go on and on without the numberline ever reaching "1".

You can't honestly still not understand this... right?

>> No.9594776

>>9594771
You are wrong though. The real numbers are defined to be the limits of equivalence classes of Cauchy sequences. Literally every single real number literally IS a limit of some sequence by its DEFINITION. We just don't include infinity because no Cauchy sequences converge to infinity.

>> No.9594779
File: 152 KB, 808x768, 1507640558145.jpg [View same] [iqdb] [saucenao] [google]
9594779

>>9594776
Fuck it, you're an idiot. This thread has been exhausting arguing with nuts but i hope at least some lurkers learned something useful for how unimportant and worse yet, poorly implemented, infinity is.

I'm out, suck my nuts.

>> No.9594789

>>9594631
If you can't even understand the concept of distance between two numbers on the real line, you've got about a decade of school before you'll learn about limits.

>> No.9594791

>>9594779
https://en.wikipedia.org/wiki/Construction_of_the_real_numbers

See construction from Cauchy sequences. It's not the best coverage, but it does also address the same points about 0.99.. and even pi.

You're literally arguing with the whole mathematical community at this point.

>> No.9594798

>>9594789
If you can't understand you imply it is infinite unending distance yet assume to finitely cover it, you've evidently skipped all education. Now fuck off, retard nigger. Get fired.

>> No.9594799

>>9594779
>I can't counter your point so I will storm off mad and assume I'm still right anyway.

>> No.9594812

>>9594799
My point remains true. Infinity is useless. It has no practical application. The arguement isn't trying to support a reason for it to exist, the arguments instead follow that the reason it isn't used for ANYTHING practical is because ITS POORLY DEFINED GARBAGE SURROUNDED BY EVEN MORE GARBAGE IDEOLOGIES WHICH REQUIRED INFINITY ALREADY BE WELL DEFINED WHEN IT NEVER, EVER WAS.

You literally ASSUME infinity makes sense when it reality it is a FUNCTIONALLY USELESS PARADOX of NONSENSE.

SUCK MY NUTS. REMAIN DUMB.

>> No.9594827

>>9594812
> It has no practical application
Yeah so? Watch me and every other mathematician not give a fuck. I am getting paid as we speak to think about things way more abstract than infinity. How does that make you feel?

>> No.9594838

>>9594771
The only thing worse than instantiating a value that can accomplish nothing is creating a methodology that invents things which themselves can accomplish nothing.

If it weren't bad enough, arithmetic solves [math]\frac{9}{10} × \infty[/math] as just already equalling infinity. The true map to the infinite limit sum 9/10^n is that 9/10 initially already equals 1. Thats your solution. You extend this a gorillion steps and think the 0.9999999.. repeating part is what is considered equating, yet really right from the getgo at 0.9, the logics of the methods had already equated this to 1.

>> No.9594841

>>9594827
Your work is unending, but your death is inevitable :^)

>> No.9594845

>>9594841
Time to have a heart attack.

>> No.9594847

>>9594838
>The true map to the infinite limit sum 9/10^n is that 9/10 initially already equals 1

Where did you get that from?

>> No.9594850

>>9594841
Of course. Death doesn't scare me.

>> No.9594855

>>9594845
Not before you suck my nuts

>> No.9594938

x is a real number
x < inf

Just defined infinity for you. How is that a poor definition? Do you know what a definition is?

>> No.9594956

>>9594367
>You can't converge to infinity
Read it again, you retarded nigger. The range converges to +1 as the Domain continues onward to infinity. It will reach all values below +1 at conditions not infinity, it will reach +1 at infinity but there will never be any condition where the sequence will result in anything > +1.

>> No.9594964

>>9594938
daily reminder

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

>> No.9594966

>>9594964
What the fuck did I say?

>> No.9594971

>>9594966
the same,
but that's just like your opinion, dude

W-A on the other hand is good, solid reference

>> No.9595075
File: 282 KB, 1440x2672, Capture+_2018-03-16-13-07-40.png [View same] [iqdb] [saucenao] [google]
9595075

>>9594971
Wolfram also says that 0.999... repeating is 1.

>> No.9595078

>>9594971
>the same,
>but that's just like your opinion, dude

You missed the point completely. The question is what's poorly defined here as it was claimed before?

>> No.9595079

>>9595075
Right. Think about it.

>> No.9595085

-1/12 only applies if you use analytic continuation. I remember being very confused about this too when I first learned about the riemann zeta but the key to note is that you're not taking the sum in the natural way.

>> No.9595090

>>9595085
>who is he talking to

>> No.9595092

>>9595079
About what?

>> No.9595221

>>9594145
>Much of the most important inventions throughout history have come from simplifying complex actions. Firearms made war and hunting more simple and faster. Vehicles made travel more simple and faster. Telecommunications made communicating more simple and faster.
you being simply ignorant doesn't mean that those actions get simplified

>> No.9595228

>>9594956
Hey brainlet. Its because you can't increment past infinity. Thats why you cant go past 1 in that case.

What you're not getting is that you also can't increment to infinity in the first place, nevermind past it. The value never even reaches 1.

0.999... isn't 1.

>> No.9595243

>>9586648
the concept of infinity was created by jews to control white people

>> No.9595245

>>9595228
Saying 0.999... is 1 is literally the same as saying $12,370 is $12,400. In real math it doesn't follow, it only follows because people dont care after a certain point. The mistake of the assumption 0.999... is 1 is in that most people dont care about decimal accuracy greater than 6 digits so any smaller decimal division ongoing may as well just round up, even though all you've done is taken an infinitely expanding number of greater and greater significant value and unfaithfully concatenated it to the inverse below a decimal where each digit instead becomes more and more insignificant.

http://m.wolframalpha.com/input/?i=x%3D10000%2C+sum%5B%289%2F10%5En%29%2C+%7Bn%2C1%2Cx%7D%5D+×10%5Ex

>> No.9595249

>>9595245
You are the mistaken one.

>> No.9595261

>>9595249
Nah, i'm really not. Compared to you, I am God. You don't even register as human. The only thing worth less than your judgement is your ignorance. Don't want to learn, go ahead, just don't expect good things to happen.

>> No.9595294

>>9595245
http://m.wolframalpha.com/input/?i=x%3D10%5E1000%2C+sum%5B%289%2F10%5En%29%2C+%7Bn%2C1%2Cx%7D%5D+×10%5Ex i think this is an example of wolfram reaching a hard value of infinity related to computer calculation rather than the allowable functional interpretation of "infinity" given the overflow message.

>> No.9595398

>>9595228
Whether or not you "reach infinity" is irrelevant, since you reach all natural numbers.

>> No.9595415

>>9595261
>stable genius has spoken

>> No.9595417

>>9595398
There are unlimited natural numbers.
There are unlimited decimal divisions between 0 and 1.
You dont reach infinity counting the integer reals.
You dont reach 1 counting the real decimals.

>>9595294
>>9595245
Click the links and enjoy your misattributed failure logic of trying to converge on infinity.

>> No.9595425
File: 223 KB, 1218x1015, 1FFD2B65-9800-48C2-AE78-A06F1FAE1CAD.jpg [View same] [iqdb] [saucenao] [google]
9595425

>>9595075
Wolfram is right, you are not

>> No.9595445

>>9595417
>There are unlimited natural numbers.
So an infinite set exists. Thanks.

>You dont reach infinity counting the integer reals.
See >>9595398

>> No.9595455

>>9595445
You are retarded. You cant reach 'all' natural numbers. You seem to have missed the potato counting example and you're trying to redefine words based on your loose grasp of the english language.

If i count potatos one by one from a bag, the bag in total is what represents all the potatos, not the amount i've counted. You dont reach all natural numbers by approaching infinity. There are always unending more numbers after any arbitrary real number. If you dont invoke any real number to start from regardless if its arbitrarily large or not, then you have not invoked to start understanding the value of infinity. All real numbers means inclusive, and if you reached all real numbers you would then reach infinity, even though this is how this works and your assumptions of how to increment are nonsense.

>> No.9595526

>>9594393
It doesn't, without axiom of infinity it just becomes a large cardinal

>> No.9595528

>>9595455
>You cant reach 'all' natural numbers.
Too late we've been doing it for hundreds of years with the calculus.

>You seem to have missed the potato counting example
Potatoes do not constrain mathematics.

>You dont reach all natural numbers by approaching infinity.
"As x approaches infinity" describes what would happen if you incremented through all the natural numbers. That's why the limit is equal to the convergent sum.

>There are always unending more numbers after any arbitrary real number. If you dont invoke any real number to start from regardless if its arbitrarily large or not, then you have not invoked to start understanding the value of infinity.
That's irrelevant to an understanding of infinity, which you lack.

>All real numbers means inclusive, and if you reached all real numbers you would then reach infinity
False, infinity is not a real number. Whether or not you can reach it is irrelevant.

>> No.9595532

>>9589351
>inffinite

>> No.9595539
File: 264 KB, 1589x646, 1484652624832.jpg [View same] [iqdb] [saucenao] [google]
9595539

>>9594240
>Which infinity?

>> No.9595543

>>9595528
The limit is infinity. The converging sum isnt infinity. You cant converge on an unknown value.

Why are you so stupid? Like it ought to be intentional, right? You're just an edgy retard who thinks you're "trolling" or something?

>> No.9595544

>>9595539
ze biiig one

>> No.9595550

>>9595543
It doesnt converge to infinity outright it just "converges" in any arbitrary value that is in place as an analog for infinity, even though "converging on infinity" is otherwise known as divergence, but because the convergence sum representation is a real number and not the infinity symbol, they pretend its somehow different.

Calculus is invalid, infinity is invalid, aleph is invalid, its all invalidates by the fact all this erroneous shit required infinity be welled defined when it wasn't. It is a house of cards and its tumbling down.

>> No.9595555

>>9595543
>The limit is infinity.
No, it's 1. Try again retard.

>> No.9595573
File: 8 KB, 477x209, 776234666555.png [View same] [iqdb] [saucenao] [google]
9595573

>>9595550
>euphoric babbling intensifies

>> No.9595603

>>9595573
Funny how infinity proves nothing too, but i guess you didn't have the foresight much less the capacity to have learned from 300 posts that infinity is worthless.

How's that 83 IQ treating you?

>> No.9595612
File: 55 KB, 617x347, 1509035736738.png [View same] [iqdb] [saucenao] [google]
9595612

>>9595555
[math]\lim_{x \rightarrow \infty} \\ \sum_{n=1}^{\infty}[/math]

>the limit is 1

>> No.9595634

http://m.wolframalpha.com/input/?i=sum%5B%28sum%5B9%2F10%5En%2C+%7Bn%2C1%2Cinfinity%7D%5D×10%5Ek%29%2C+%7Bk%2C1%2Cinfinity%7D%5D

"Converges" to 1 under the decimal but "diverges" to infinity over the decimal. Wew.

Only with infinity could something as retarded as two different terms for the exact identical function arisen.

>> No.9595972

>>9595634
http://m.wolframalpha.com/input/?i=lim+n+to+k%2C+%28lim+k+to+infinity%2C+%281-2%5E-k%29×n%29
>wen u simulataneously converge on all reals while diverging to infinity
Like dis post if u cri everi tiem

>> No.9596003

>>9595612
That's not the limit we're taking about. Just stop posting, this is pathetic.

>> No.9596018

>>9595634
>>9595972
I can't even imagine how dumb you must be to think this supports your argument. You might have a mental defect if you're this delusional.

>> No.9596023
File: 87 KB, 487x473, CzYzJOBUkAAMjRK-1.jpg [View same] [iqdb] [saucenao] [google]
9596023

>>9595972
http://m.wolframalpha.com/input/?i=sum%5B+sum%5B%28k%2F%28k%2B1%29%5En%29%2C+%7Bn%2C1%2Cinfinity%7D%5D%2C+%7Bk%2C1%2Cinfinity%7D%5D

>> No.9596033

>>9596018
You're delusional if you think the angle at which you approach infinity ought to differentiate convergence from divergence. Doesn't matter how you approach infinity, you never reach it

>> No.9596062

>>9596033
0.999••• of all reals is no closer to infinity than 0 when you have unlimited reals
0.999••• of 1 is no closer to 1 than 0 when you have unlimited decimal places

>> No.9596358

>>9596033
>You're delusional if you think the angle at which you approach infinity ought to differentiate convergence from divergence.
n approaches approaches infinity the same way every time, convergence is determined by the function on n. You just can't stop making a fool of yourself with these retarded statements.

>Doesn't matter how you approach infinity, you never reach it
See >>9595445

>> No.9596364

>>9596358
See>>9595455

>> No.9596370

>>9596062
>0.999••• of all reals
Gibberish

>0.999••• of 1 is no closer to 1 than 0
Wrong

Try again.

>> No.9596377

>>9596364
See >>9595528

>> No.9596403

>>9596377
>>9596370
Hey retard, you can't reach infinity. Id you only assume reals, then 0.999••• can inlt have arbitrarily real number of 9's.

Good job flip flopping faggot. You honestly dont know anything and were pinned down from the get go.

>> No.9596446

>>9595425
Of course it's right. Also how can I not be right if I agree with wolfram and it's right?

>> No.9596450

>>9596403
>Hey retard, you can't reach infinity.
See >>9596358

>Id you only assume reals, then 0.999••• can inlt have arbitrarily real number of 9's.
This just shows your complete ignorance of what you're talking about. The construction of the real numbers leads to their completeness, which is equivalent to the statement that all real numbers have corresponding infinite string decimal representations. So "assuming the reals" implies exactly what you're trying to argue against. The fact that you haven't figured out by now that the construction of the reals requires infinity or infinite choice is truly pathetic.

>> No.9596473

>>9596403
This whole talk about reaching infinity shows you have no idea what limits are about.

>> No.9596591

>>9596473
Infinity is useless.
Therefore, everything that implements infinity is also useless.
Argue with reality, i don't give a shit.

>> No.9596605

>>9596591
Your opinion about the usefulness of infinity doesn't change your ignorance of limits.

>> No.9596748

>>9596605
Actually it reinforces his ignorance of limits.

>> No.9596763
File: 73 KB, 500x308, 1518192771498.jpg [View same] [iqdb] [saucenao] [google]
9596763

>>9587117
You typed all of that for nothing.

Infinity is just short for "always greater than". That is its purpose.