/sci/ - Science & Math » Thread #13605150

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Anonymous Sun 05 Sep 06:16:59 2021 No.13605150 View Reply Original Report

Quoted By: >>13605227 >>13605235 >>13605273 >>13605301 >>13607462 >>13608964 >>13609014 >>13609173

>3*3=9
>3*3.333...=10
>3*3.666...=11
>3*3.999...=12
>3*4=12
How does math reconcile this?
3.999... is not equal to 4 yet the give the same answer

Anonymous

Anonymous Sun 05 Sep 2021 06:36:44 No.13605174 Report

Quoted By: >>13610028

Everyone else has had more sex than me, does anyone else get that feeling?

Anonymous

Anonymous Sun 05 Sep 2021 06:59:33 No.13605227 Report

Quoted By:

>>13605150
>How
1/inf=0

Anonymous

Anonymous Sun 05 Sep 2021 07:04:01 No.13605235 Report

Quoted By: >>13605237 >>13611638

>>13605150
>3.999... is not equal to 4
wrong

Anonymous

Anonymous Sun 05 Sep 2021 07:05:59 No.13605237 Report

Quoted By: >>13605248 >>13605266

>>13605235
Theyre different numbers
What we can just round everything up to the next infinitesimal?
Then why doesnt everything equal everything?

Anonymous

Anonymous Sun 05 Sep 2021 07:19:33 No.13605248 Report

Quoted By: >>13609475

>>13605237
>Theyre different numbers
prove it
>next infinitesimal?
no such thing in real numbers

Anonymous

Anonymous Sun 05 Sep 2021 07:28:28 No.13605266 Report

Quoted By:

>>13605237
4 and 3.999... are equal
1/3 = .333...
2/3 = .666...
3/3 = 1 = 3 * 1/3 = .999...
the difference between them is not even infinitesimal; it is zero. they are the same number, just written in different ways

Anonymous

Anonymous Sun 05 Sep 2021 07:31:17 No.13605273 Report

Quoted By:

>>13605150
>3.999... is not equal to 4
Those nines go on forever. There is no number between 3.999... and 4. What's a number such that there is no other number between it and 4?

Anonymous

Anonymous Sun 05 Sep 2021 07:46:51 No.13605301 Report

Quoted By: >>13608918

>>13605150

x = 3.999...
10x = 39.999...
10x - x = 9x = 36
x = 4

use google next time and stop getting filtered by rational numbers retard

Anonymous

Anonymous Sun 05 Sep 2021 21:18:02 No.13607462 Report

Quoted By: >>13608388 >>13608918

>>13605150
$3\times 3.999...=3\times(3+0.999...)$
$x=0.999... \implies 10x=9.999...\implies 9x=9\implies x=1 \\$

$3\times(3+0.999...)=3\times(3+1)$
$3\times(3+1)=12$

Anonymous

Anonymous Mon 06 Sep 2021 03:31:41 No.13608388 Report

Quoted By: >>13608885

>>13607462
That doesn't follow

Anonymous

Anonymous Mon 06 Sep 2021 08:31:46 No.13608885 Report

Quoted By:

>>13608388
which implication?

Anonymous

Anonymous Mon 06 Sep 2021 08:47:09 No.13608918 Report

Quoted By: >>13608960

>>13605301
>>13607462
Doesn't really prove anything. Merely demonsrates consistency for specific cases. You need to prove consistency in all cases.

Anonymous

Anonymous Mon 06 Sep 2021 09:10:18 No.13608960 Report

Quoted By: >>13608966

>>13608918
proves 3*0.999... = 12

Anonymous

Anonymous Mon 06 Sep 2021 09:11:14 No.13608964 Report

Quoted By: >>13608969 >>13608987

>>13605150
Consider
$a_n = 3 + \frac{1}{10^{n+1}}\sum_{k=0}^n 9\cdot10^k=3 + \frac{9}{10^{n+1}}\frac{10^{n+1}-1}{10-1} = 3 + 1 - \frac{1}{10^{n+1}} = 4 - \frac{1}{10^{n+1}}$
Of course for all $n\in\mathbb{N}$ : $a_n\leq4$ and $a_n\leq a_{n+1}$ so the series converges. There are many other ways of finding the limit but let's just agree that $\lim a_n = 4 - \lim\frac{1}{10^{n+1}} = 4$ .

If you don't think this is clear proof that 3.999...=4 then you probably don't understand how infinite things work. You probably don't agree with $\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\cdots = 1$ either right? If that is really the case don't visit /sci/ again.

Anonymous

Anonymous Mon 06 Sep 2021 09:11:55 No.13608966 Report

Quoted By: >>13608970

>>13608960
You can prove anything if you have an inconsistency.

Anonymous

Anonymous Mon 06 Sep 2021 09:14:19 No.13608969 Report

Quoted By: >>13608981

>>13608964
>If you don't think this is clear proof that 3.999...=4
Not OP, and I don't dispute that 3.999...=4, but your "proof" isn't really a proof.

Anonymous

Anonymous Mon 06 Sep 2021 09:14:19 No.13608970 Report

Quoted By: >>13608975

>>13608966
what inconsistency?

Anonymous

Anonymous Mon 06 Sep 2021 09:15:20 No.13608975 Report

Quoted By: >>13608980 >>13608982 >>13609487 >>13610131

>>13608970
>what inconsistency?
The inconsistency of equating two numbers that aren't actually the same number.

Anonymous

Anonymous Mon 06 Sep 2021 09:18:04 No.13608980 Report

Quoted By:

>>13608975
>i don't like the result
hurr durr

Anonymous

Anonymous Mon 06 Sep 2021 09:18:10 No.13608981 Report

Quoted By:

>>13608969
>isn't really a proof.
You're delusional. Your understanding of math is flawed. Go write a book that's 300 pages long giving the proof that the chances of getting tails is 1/2 or something.

Anonymous

Anonymous Mon 06 Sep 2021 09:18:16 No.13608982 Report

Quoted By: >>13609075

>>13608975
that's an inconsistency only if you can prove that the two numbers are really distinct. proof by "they look different to me" doesn't count.

Anonymous

Anonymous Mon 06 Sep 2021 09:19:28 No.13608987 Report

Quoted By: >>13608997

>>13608964
>you probably don't understand how infinite things work
do you? can you explain what is a set?

Anonymous

Anonymous Mon 06 Sep 2021 09:23:01 No.13608997 Report

Quoted By: >>13609007

>>13608987
>do you?
Yes.
>can you explain what is a set?
Yes, a collection of things.

Your problem is that my answer won't satisfy your midwit beliefs.
You're the kind of guy who is amazed by the fact that the fib sequence describes so many natural phenomenons, that euler's number is around 2.7 and that the universe works with math.
Listen up, math is a construct and they are right because we agree they are right. That's the whole point of axioms.

Anonymous

Anonymous Mon 06 Sep 2021 09:25:38 No.13609007 Report

Quoted By: >>13609012

>>13608997
>Yes, a collection of things.
So the collection of all groups is a set, correct?

Anonymous

Anonymous Mon 06 Sep 2021 09:27:22 No.13609012 Report

Quoted By: >>13609016

>>13609007
To be honest I don't understand your questions because I don't know your terminology and definitions.
But why not? Why shouldn't it be a set? I don't care about names.

Anonymous

Anonymous Mon 06 Sep 2021 09:29:04 No.13609014 Report

Quoted By: >>13609021

>>13605150
>3.999... is not equal to 4
it is. because the difference is infinitesimal, exactly what 0 is.

Anonymous

Anonymous Mon 06 Sep 2021 09:29:55 No.13609016 Report

Quoted By: >>13609021

>>13609012
>collection of all groups is a set
Looks like you don't understand how infinite things work after all.

Anonymous

Anonymous Mon 06 Sep 2021 09:30:47 No.13609021 Report

Quoted By: >>13609040

>>13609016
So now we're equal!

>>13609014
>the difference is infinitesimal, exactly what 0 is.
Not really but you agree that 3.999... = 4 so we're cool.

Anonymous

Anonymous Mon 06 Sep 2021 09:39:39 No.13609040 Report

Quoted By: >>13609050 >>13609059

>>13609021
>Not really
What's the difference? How can you even theoretically distinguish one from the other?

Anonymous

Anonymous Mon 06 Sep 2021 09:43:48 No.13609050 Report

Quoted By:

>>13609040
Based on wiki "an infinitesimal or infinitesimal number is a quantity that is closer to zero than any standard real number, but that is not zero". However, given that definition I can understand how someone could argue that infinitesimal is zero, but at the same time you can't because by definition it is not.

I guess using "infinitesimal" is a great way to intuitively understand things like 0.99...=1 but I wouldn't agree that it is a rigorous way.

Anonymous

Anonymous Mon 06 Sep 2021 09:50:43 No.13609059 Report

Quoted By:

>>13609040
an infinitesimal is something non-zero but smaller than every "usual" number. there are no infinitesimals in the real numbers, but there are other number systems where infinitesimals exist. the existence of infinitesimals doesn't automatically mean 3.999.. < 4 though, that depends on the precise definition of 3.999...

Anonymous

Anonymous Mon 06 Sep 2021 09:59:34 No.13609075 Report

Quoted By: >>13609082

>>13608982
>that's an inconsistency only if you can prove that the two numbers are really distinct
You're the one who set out to prove that they're the same number. I'm just telling you that's not a way to do it, because all you're demonstrating is that it doesn't cause any apparent inconsistency in one specific case.

Anonymous

Anonymous Mon 06 Sep 2021 10:03:13 No.13609082 Report

Quoted By: >>13609120

>>13609075
>You're the one who set out to prove that they're the same number
x = 3.999...
10x = 39.999...
10x - x = 39.999... - 3.999...
9x = 36
x = 4

Anonymous

Anonymous Mon 06 Sep 2021 10:24:20 No.13609120 Report

Quoted By: >>13609125

>>13609082
Again, that only proves consistency in one specific case.

Anonymous

Anonymous Mon 06 Sep 2021 10:26:49 No.13609125 Report

Quoted By: >>13609134

>>13609120
what specific case?

Anonymous

Anonymous Mon 06 Sep 2021 10:31:41 No.13609134 Report

Quoted By: >>13609154

>>13609125
The specific case of those particular algebraic manipulations.

Anonymous

Anonymous Mon 06 Sep 2021 10:41:31 No.13609154 Report

Quoted By: >>13609211 >>13609224 >>13609245

>>13609134
so you're saying that

x = 0.999...
x = lim_{n->inf} sum_{k=1}^n 9/10^k
x = lim_{n->inf} 1 - 1/10^n
x = 1

also doesn't prove 0.999.. = 1, it only proves consistency in this specific case.

Anonymous

Anonymous Mon 06 Sep 2021 10:48:16 No.13609173 Report

Quoted By:

>>13605150
the calculator need a minimum 10 length of 9 string like so
3.9999999999
to result 12, do it on paper it will result something else this is just a software limitation

Anonymous

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Anonymous Mon 06 Sep 2021 10:57:06 No.13609192 Report

Quoted By:

>3*3=9
>3*3.3=10
>3*3.6=11
>3*3.9=12
>3*4=12
How does math reconcile this?
3.9 is not equal to 4 yet the give the same answer

Anonymous

Anonymous Mon 06 Sep 2021 11:08:33 No.13609211 Report

Quoted By: >>13609214 >>13609224

>>13609154
I'm saying that algebraic manipulations don't really prove anything. You can use them to get all kinds of spurious results for division by 0, and the only way out of that is to disallow division by 0 altogether, on the grounds that it always causes inconsistencies. Your algebraic manipulations rely on the assumption that you can do normal arithmetic on 3.999..., and that doing so doesn't introduce inconsistencies, which itself relies on the assumption that 3.999... is just a fancy way to write 4. As for using limits, that's basically begging the question, because one could question whether or not the leap from "X approaches Y as Z tends to infinity" to "the value is Z" is justified. I think it is justified, but you sure as fuck have not proven it here.

Anonymous

Anonymous Mon 06 Sep 2021 11:09:44 No.13609214 Report

Quoted By:

>>13609211
the value is Y*

Anonymous

Anonymous Mon 06 Sep 2021 11:17:05 No.13609224 Report

Quoted By: >>13609229

>>13609211
so you're saying that >>13609154 is not a valid proof of 0.999... = 1

Anonymous

Anonymous Mon 06 Sep 2021 11:19:25 No.13609229 Report

Quoted By: >>13609245

>>13609224
I'm saying it's not a proof in the context where someone questions 0.999... = 1 on grounds that apply to limits themselves.

Anonymous

Anonymous Mon 06 Sep 2021 11:29:42 No.13609245 Report

Quoted By: >>13609248

>>13609229
like what? which implication in >>13609154 is not clear?

Anonymous

Anonymous Mon 06 Sep 2021 11:32:35 No.13609248 Report

Quoted By: >>13609259

>>13609245
Whether or not the fourth line actually follows from the 3rd depends on whether or not you accept the reasoning behind limits.

Anonymous

Anonymous Mon 06 Sep 2021 11:44:06 No.13609259 Report

Quoted By: >>13609268

>>13609248
so "that only proves consistency in one specific case" is supposed to mean "you haven't proved lim_{n->inf} 1 - 1/10^n = 1"

Anonymous

Anonymous Mon 06 Sep 2021 11:47:40 No.13609268 Report

Quoted By: >>13609286

>>13609259
No. "that only proves consistency in one specific case" refers to your attempt at a "proof" through algebraic manipulation.

Anonymous

Anonymous Mon 06 Sep 2021 11:54:35 No.13609286 Report

Quoted By: >>13609287

>>13609268
which implication in the algebraic proof is not clear?

Anonymous

Anonymous Mon 06 Sep 2021 11:55:31 No.13609287 Report

Quoted By: >>13609288

>>13609286
All of it is clear and none of it is a proof. I love how this board is chock full of sub-90-IQ spergs.

Anonymous

Anonymous Mon 06 Sep 2021 11:56:33 No.13609288 Report

Quoted By:

>>13609287
if all implications are clear, then it's a valid proof. insulting the whole board doesn't change this.

Anonymous

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Anonymous Mon 06 Sep 2021 13:15:55 No.13609450 Report

Quoted By: >>13609483

Anonymous

Anonymous Mon 06 Sep 2021 13:27:34 No.13609475 Report

Quoted By: >>13610708

>>13605248
look up nonstandard analysis

Anonymous

Anonymous Mon 06 Sep 2021 13:32:43 No.13609483 Report

Quoted By: >>13609520 >>13610020

>>13609450
Can you actually prove that bs?

Anonymous

Anonymous Mon 06 Sep 2021 13:36:15 No.13609487 Report

Quoted By:

>>13608975
Are 5, 25/25 and 10 in base 5 all different numbers?

Anonymous

Anonymous Mon 06 Sep 2021 13:49:29 No.13609520 Report

Quoted By: >>13610125

>>13609483
$ \boxed{0 1 = p + (1-p) ~~~~~~ \overset{1}{ \overbrace{[=====p=====|==(1-p)==]}} \\ \text{divide p using x} ~~~~~~ \overset{1}{ \overbrace{ \underset{p}{[ \underbrace{=====x=====|==(p-x)==}]} ~~ + ~~ (1-p)}} \\ \\ \text{solve x and (p-x), when length ratios must be the same} \\ \dfrac{x}{p-x}= \dfrac{p}{1-p} \Rightarrow x- xp = p^2 - xp \Rightarrow \underline{x=p^2} \Rightarrow \underline{(p-x)=p(1-p)} \\ \overset{1}{ \overbrace{ \underset{p}{[ \underbrace{=====p^2=====|==p(1-p)==}]} ~~ + ~~ (1-p)}} \\ \\ \overset{1}{ \overbrace{ \underset{p^2}{[ \underbrace{=====p^3=====|==p^2(1-p)==}]} ~~+ p(1-p)+(1-p)}} \\ \overset{1}{ \overbrace{ \underset{p^3}{[ \underbrace{=====p^4=====|==p^3(1-p)==}]} ~~+ p^2(1-p)+p(1-p)+(1-p)}} \\ (1-p)+p(1-p)+p^2(1-p)+p^3(1-p)+ \cdots =1 ~~~~ \left | ~ \times \frac{1}{1-p} \right . \\ 1+p+p^2+p^3+ \cdots = \dfrac{1}{1-p} $

Anonymous

Anonymous Mon 06 Sep 2021 16:14:02 No.13610020 Report

Quoted By:

>>13609483
yes

Anonymous

Anonymous Mon 06 Sep 2021 16:18:42 No.13610028 Report

Quoted By: >>13610030

>>13605174
Don’t worry anon, they are the real uncles all long

Anonymous

Anonymous Mon 06 Sep 2021 16:19:44 No.13610030 Report

Quoted By:

>>13610028
Fuck I meant to say incels

Anonymous

Anonymous Mon 06 Sep 2021 16:58:24 No.13610125 Report

Quoted By: >>13610155

>>13609520
I have never seen it proved like this, kek

Anonymous

Anonymous Mon 06 Sep 2021 17:02:32 No.13610131 Report

Quoted By:

>>13608975
That's the confusion around infinity, your mind wants to end the string of 9's which makes this equality seem logically implausible.

Anonymous

Anonymous Mon 06 Sep 2021 17:11:20 No.13610155 Report

Quoted By:

>>13610125
https://youtu.be/XFDM1ip5HdU?t=5m20s

Anonymous

Anonymous Mon 06 Sep 2021 19:51:53 No.13610708 Report

Quoted By: >>13611606

>>13609475
>nonstandard analysis
Learn to read and stop talking about shit you don't understand.

Anonymous

Anonymous Tue 07 Sep 2021 02:16:32 No.13611606 Report

Quoted By:

>>13610708
>don't talk about shit i don't understand
lol

anyways it's the same number in the reals but not in the hyperreals

the standard part of this
4 - epsilon is just 4
on the other hand in the hyperreals it's different from 4

since 4- epsilon - 4 = -epsilon
which is not zero, rather infinitesimal
it's only when you collapse to the reals that it becomes zero.

on the other hand, you have several series that converge to the same number, therefore you have several decimal representations for any given number

Anonymous

Anonymous Tue 07 Sep 2021 02:26:08 No.13611631 Report

Quoted By:

>20 posters
>64 posters

Anonymous

Anonymous Tue 07 Sep 2021 02:30:21 No.13611638 Report

Quoted By: >>13611670

>>13605235
Different representations of the same value have the same value.

Anonymous

Anonymous Tue 07 Sep 2021 02:41:07 No.13611670 Report

Quoted By: >>13612006

>>13611638
different infinite series converge to the same value

4+0+0+0+0.... =
3+0.9+0.09+...

They only are equal in the limit. Stop short and they're different.

Anonymous

Anonymous Tue 07 Sep 2021 04:51:39 No.13612006 Report

Quoted By:

>>13611670
>let's pretend finite is infinite

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