/sci/ - Science & Math » Thread #13719450

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0.9999... = 1 - Proof for the Retarded

Anonymous Tue 05 Oct 19:33:46 2021 No.13719450 View Reply Original Report

Quoted By: >>13719456 >>13719459 >>13719564 >>13719598 >>13719632 >>13719726 >>13719744 >>13720014 >>13721247 >>13721500 >>13723046 >>13725673 >>13726086 >>13726733 >>13728228

There's 0.9999... of them in every thread: retards who don't understand how infinite series work. If they passed Algebra 2, they can follow this proof (pic related). Anyone who still doesn't understand it is a troll and shouldn't be fed.

Anonymous

Anonymous Tue 05 Oct 2021 19:35:35 No.13719456 Report

Quoted By: >>13720908

>>13719450
Literally doesn't prove anything.

Anonymous

Anonymous Tue 05 Oct 2021 19:35:54 No.13719459 Report

Quoted By: >>13719500 >>13719569 >>13719615 >>13722229 >>13722775

>>13719450
I mean it's just definitions bro. You can make 0.9999..... != 1 if you like. There are number systems that do like the surreal numbers. The idea that you can prove shit like this is kinda dumb

Anonymous

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Anonymous Tue 05 Oct 2021 19:37:44 No.13719465 Report

Quoted By: >>13719472 >>13722876

Anonymous

Anonymous Tue 05 Oct 2021 19:39:39 No.13719472 Report

Quoted By: >>13719482 >>13719487

>>13719465
OP here. I like this one better because I'm not retarded. Original proof is HS algebra for the plebs.

Anonymous

Anonymous Tue 05 Oct 2021 19:41:05 No.13719482 Report

Quoted By: >>13719509

>>13719472
Stop being so elitist you autist

Anonymous

Anonymous Tue 05 Oct 2021 19:42:40 No.13719487 Report

Quoted By: >>13719503 >>13719511

>>13719472
>Original proof
That's not a proof. You literally make an arbitrary leap half way through.

Anonymous

Anonymous Tue 05 Oct 2021 19:46:19 No.13719500 Report

Quoted By:

>>13719459
Sure. The trick is to make sure your definitions don't lead to contradictions in other areas of mathematics. Math is not just a vast toolbox of tricks and techniques; math is a way of thinking: the art of non-contradictory identification. If the value assigned to the limit that's represented by 0.9999... is not equal to 1, then the method by which you do assign a particular value has to be consistent with the way you assign finite values to convergent finite series.

Anonymous

Anonymous Tue 05 Oct 2021 19:47:20 No.13719503 Report

Quoted By: >>13719508

>>13719487
Which step? Genuinely curious.

Anonymous

Anonymous Tue 05 Oct 2021 19:48:47 No.13719508 Report

Quoted By: >>13719522 >>13719576

>>13719503
>6th to 7th line
>trust me, bro

Anonymous

Anonymous Tue 05 Oct 2021 19:48:53 No.13719509 Report

Quoted By: >>13719520 >>13721935

>>13719482
>elitist
>"I'm not sad that people are smarter than I am, but I am sad that they know it and aren't apologizing for it."

kys

Anonymous

Anonymous Tue 05 Oct 2021 19:49:14 No.13719511 Report

Quoted By:

>>13719487
>arbitrary leap half way through
where

Anonymous

Anonymous Tue 05 Oct 2021 19:50:12 No.13719514 Report

Quoted By: >>13719525

Dumb kiddies

Anonymous

Anonymous Tue 05 Oct 2021 19:51:27 No.13719520 Report

Quoted By: >>13719556 >>13728019

>>13719509
Bro be a dickhead if you like, but don't expect anyone to like you or want to work with you. Just because you've worked hard in a subject to get far, doesn't mean you are superior to others. It's just you have different interests and that's fine.

Anonymous

Anonymous Tue 05 Oct 2021 19:51:48 No.13719522 Report

Quoted By: >>13719533 >>13719576

>>13719508
>6th to 7th line
That's just the formula for the sum of an infinite geometric series applied to this expression where r = 1/10 and a_1 = 1/10.
https://people.richland.edu/james/lecture/m116/sequences/geometric.html
>trust me bro
kek, yeah exactly.

Anonymous

Anonymous Tue 05 Oct 2021 19:52:49 No.13719525 Report

Quoted By:

>>13719514
My point exactly.

Anonymous

Anonymous Tue 05 Oct 2021 19:54:03 No.13719533 Report

Quoted By: >>13719537 >>13719597

>>13719522
>That's just the formula for the sum of an infinite geometric series applied to this expression
I know, and the point still stands.

Anonymous

Anonymous Tue 05 Oct 2021 19:55:25 No.13719537 Report

Quoted By: >>13719538 >>13719542

>>13719533
Why does it still stand? Why is it an arbitrary leap? Be more specific.

Anonymous

Anonymous Tue 05 Oct 2021 19:57:21 No.13719538 Report

Quoted By: >>13719547 >>13719562

>>13719537
Because they haven't proven the formula. But it's fairly easy to show that it's bounded above using induction, and increasing, so limit exists. Then you can manipulate the sum and quite easily get the result.

Anonymous

Anonymous Tue 05 Oct 2021 19:58:06 No.13719542 Report

Quoted By: >>13719562

>>13719537
>Why is it an arbitrary leap?
Because you've not provided any proof for it.

Anonymous

Anonymous Tue 05 Oct 2021 19:59:08 No.13719547 Report

Quoted By: >>13719553 >>13719562

>>13719538
>so limit exists
People who don't accept 0.9999... = 1 won't accept limits by exactly the same token.

Anonymous

Anonymous Tue 05 Oct 2021 20:01:31 No.13719553 Report

Quoted By: >>13719562 >>13719563

>>13719547
I mean the typical definition of reals uses limits in some form. Using equivalence classes of cauchy sequences which explicitly uses limits. You need to have some definition of the reals you are willing to work with in order to prove anything about them. So like, I guess if they aren't willing to accept limits, they just aren't willing to accept the standard definition of the reals, which is fine, but it means that no proof given here is valid for them.

Anonymous

Anonymous Tue 05 Oct 2021 20:03:26 No.13719556 Report

Quoted By: >>13719566

>>13719520
>don't expect anyone to like you or want to work with you
>"But people won't LIKE you!!!"

So the moral appraisal of yourself by others is a primary concern which supersedes truth, facts, reason, and logic? Is the disapproval of others so earth-shatteringly terrifying that you cannot conceive of such a monster that cares more about what's true than what the masses of oxygen-thieves say is true? You do you, bro. You do you.

>Just because you've worked hard in a subject to get far, doesn't mean you are superior to others.

That's exactly what it means. My chosen field built the first world and illuminates every corner of reality besides. I'm perfectly happy to acknowledge the relative superiority of other mathematicians' skills over my own, but that still doesn't preclude me feeling proud (rightly so) of being better than those who don't know any math. You'd rather I'd be humble to protect your feelings; I'd rather give the finger to your feelings.

Anonymous

Anonymous Tue 05 Oct 2021 20:04:57 No.13719562 Report

Quoted By:

>>13719538
>>13719542
>>13719547
>>13719553

Welcome to the conversation! Let's keep asking "but why? but why? but why?" and get to the heart of the matter instead of slinging poo. I like it.

Anonymous

Anonymous Tue 05 Oct 2021 20:04:59 No.13719563 Report

Quoted By:

>>13719553
>the typical definition of reals uses limits in some form
The people who are serious about denying 0.9999... = 1 reject the reals, too.

Anonymous

Anonymous Tue 05 Oct 2021 20:05:29 No.13719564 Report

Quoted By:

>>13719450
Yep. This is trivial shit from undergrad calculus.

Anonymous

Anonymous Tue 05 Oct 2021 20:06:39 No.13719566 Report

Quoted By: >>13719636

>>13719556
I mean if you want to collaborate with people on mathematics you need them to like you enough to enjoy working with you? Frankly you come off as incredibly ignorant of other fields if you think that mathematics was the only subject that "built the first world". You'll probably grow up with time, I just hope you're not like in your 20s or something

Anonymous

Anonymous Tue 05 Oct 2021 20:07:21 No.13719569 Report

Quoted By: >>13719574

>>13719459
No one who thinks .999...=/=1 knows what the Surreals are. Stop giving these morons who flunked out of calc. the benefit of the doubt.

Anonymous

Anonymous Tue 05 Oct 2021 20:10:08 No.13719574 Report

Quoted By:

>>13719569
You're kinda missing my point that you need to have some formal axiomatic system your statements are being evaluated in to be able to prove anything. Most people don't have an axiomatic model of mathematics but just go on intuition. That's fine because after all our axiomatic models are developed following intuition. But like to prove it by making assumptions about limits and shit is imposing a model that the person you're proving stuff to doesn't necessarily agree with. And there's no reason that the particular model you're suggesting is the correct one, as opposed to another one like the surreals

Anonymous

Anonymous Tue 05 Oct 2021 20:10:57 No.13719576 Report

Quoted By: >>13719579 >>13719583

>>13719522
He means the posted proof with the limit definition, not your original post.

>>13719508
Between lines 6 and 7, the step can be conceptualized by trying out different specific values of n and N to convince yourself that the inequality holds, as long as n>=N and N is taken to be the definition given in between (6) and (7).

Anonymous

Anonymous Tue 05 Oct 2021 20:12:29 No.13719579 Report

Quoted By:

>>13719576
Ah, I gotcha. Thx

Anonymous

Anonymous Tue 05 Oct 2021 20:13:48 No.13719583 Report

Quoted By:

>>13719576
>He means the posted proof with the limit definition
No, I actually did mean his original post.

Anonymous

Anonymous Tue 05 Oct 2021 20:17:23 No.13719597 Report

Quoted By: >>13719609 >>13719617

>>13719533
Huh. It's almost like you could look up the proof yourself and follow the derivation. I guess that's my fault for thinking you'd have enough initiative to do that yourself in the age of ubiquitous near-instantaneous transfer of information via the Internet. Here you go, I'll spoon-feed you this time. Open wide! Here comes the airplane!!!

https://math.stackexchange.com/questions/370662/infinite-geometric-series-formula-derivation

Anonymous

Anonymous Tue 05 Oct 2021 20:17:25 No.13719598 Report

Quoted By: >>13719912

>>13719450
0.999... is not real and do not exist

Anonymous

Anonymous Tue 05 Oct 2021 20:20:14 No.13719609 Report

Quoted By:

>>13719597
anon irl https://www.youtube.com/watch?v=q9Ui0F9115w

Anonymous

Anonymous Tue 05 Oct 2021 20:21:04 No.13719615 Report

Quoted By: >>13719622

>>13719459
$0.999\ldots = 1$ in the surreals as well. What you really mean is $0.999\ldots_\omega 000... < 0.999\ldots = 1$ , which is different.

Anonymous

Anonymous Tue 05 Oct 2021 20:21:26 No.13719617 Report

Quoted By:

>>13719597
>It's almost like you could look up the proof yourself
But I thought all I needed was your "proof". So you've proven nothing, and are now referring me to another proof that someone would question on the same grounds that they use to question what you're trying to prove in the first place.

Anonymous

Anonymous Tue 05 Oct 2021 20:22:28 No.13719622 Report

Quoted By:

>>13719615
Oh. I always have said the surreal thing without knowing the surreals lol. I think I must have heard someone else say it and just assumed it true or like misinterpreted. Thanks.

Anonymous

Anonymous Tue 05 Oct 2021 20:28:16 No.13719632 Report

Quoted By: >>13719633 >>13719640 >>13726080

>>13719450
How about the
$0.999\dots = 0.333\dots + 0.333\dots + 0.333\dots$
$0.999\dots =\frac{1}{3}+\frac{1}{3} + \frac{1}{3}$
$0.999\dots =3 \frac{1}{3}$
$0.999\dots =1$
proof?

Anonymous

Anonymous Tue 05 Oct 2021 20:28:46 No.13719633 Report

Quoted By: >>13719637

>>13719632
No there's a 4 at the end of the rainbow dummy

Anonymous

Anonymous Tue 05 Oct 2021 20:29:50 No.13719636 Report

Quoted By: >>13719644

>>13719566
Hate to break it to you, but /sci is not the place to collaborate with people on mathematics. Gotta go to meatspace for that. If you think I speak to anyone worth talking to IRL like I do on 4chan, then I have some prime real estate in Florida's best swampland to sell you.

Anonymous

Anonymous Tue 05 Oct 2021 20:30:19 No.13719637 Report

Quoted By:

>>13719633
prove it or you geh

Anonymous

Anonymous Tue 05 Oct 2021 20:30:51 No.13719640 Report

Quoted By: >>13719643

>>13719632
If you don't believe that 1=0.999..., then you don't believe that 1/3=0.333... either.

Anonymous

Anonymous Tue 05 Oct 2021 20:31:55 No.13719643 Report

Quoted By: >>13719657

>>13719640
right.
why periodic decimals bothers the schizo /x/ tards so much?

Anonymous

Anonymous Tue 05 Oct 2021 20:31:55 No.13719644 Report

Quoted By:

>>13719636
I too am just pretending to be retarded

Anonymous

Anonymous Tue 05 Oct 2021 20:38:33 No.13719657 Report

Quoted By: >>13719661 >>13719679

>>13719643
It just circles back to the issue that you're trying to assign a value to an infinite expression, as if you could somehow get to the end of something endless.

Anonymous

Anonymous Tue 05 Oct 2021 20:39:32 No.13719661 Report

Quoted By: >>13719667

>>13719657
ah yeah, but convergence is actually a thing

Anonymous

Anonymous Tue 05 Oct 2021 20:41:54 No.13719667 Report

Quoted By:

>>13719661
They'll accept that you can get arbitrarily close to 1/3, but never actually get to 1/3, and it's not that hard to see their point.

Anonymous

Anonymous Tue 05 Oct 2021 20:46:33 No.13719679 Report

Quoted By: >>13719693

>>13719657
Did you take calculus? How about real analysis?

Anonymous

Anonymous Tue 05 Oct 2021 20:50:13 No.13719693 Report

Quoted By:

>>13719679
I don't have a problem with 0.999... = 1. I'm just telling you why some people have a problem with it, and why they're not convinced.

Anonymous

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Anonymous Tue 05 Oct 2021 21:05:07 No.13719726 Report

Quoted By: >>13719803 >>13719871 >>13719881 >>13719891

>>13719450

Anonymous

Anonymous Tue 05 Oct 2021 21:10:53 No.13719744 Report

Quoted By:

>>13719450
0.9999.... > 1

There, I just ended your theory without a bunch of nerd shit

Anonymous

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Anonymous Tue 05 Oct 2021 21:17:25 No.13719762 Report

Quoted By: >>13721430

Hmm, interestingly, coding only needs 17 iterations to make it 1

Anonymous

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Anonymous Tue 05 Oct 2021 21:31:21 No.13719803 Report

Quoted By: >>13720023 >>13725637 >>13725648

>>13719726
Makes me think...

Anonymous

Anonymous Tue 05 Oct 2021 21:54:31 No.13719871 Report

Quoted By: >>13719898 >>13720072

>>13719726
the " $\dots$ " translates to "there's a pattern in the expression and I will not waste my time writting down huge ammounts of them because it's stupid doing it"

which is different to the schizoid interpretation "then something unkown, unintelligible, magical, mysterious, way-beyond-our-mundane-comprehensions of things and their abstractions happens here, so I cannot recognize that such obscure thing as a something can exist if cannot look at it by my self" because, indeed, you can, it will only take a huge amount of time to write down an expression that can convince them and in the end will not be much gain for no one.

Anonymous

Anonymous Tue 05 Oct 2021 21:57:47 No.13719881 Report

Quoted By:

>>13719726
$0.999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999$

Anonymous

Anonymous Tue 05 Oct 2021 22:00:28 No.13719891 Report

Quoted By: >>13721552

>>13719726
$0.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 \text{ reply or your mom will die in her sleep tonight}$

Anonymous

Anonymous Tue 05 Oct 2021 22:02:28 No.13719898 Report

Quoted By: >>13719987

>>13719871
>it will only take a huge amount of time to write down an expression that can convince them
They'll be convinced when you finish writing down all of that infinite expression. I don't know. You seem to suffer from genuine mental retardation.

Anonymous

Anonymous Tue 05 Oct 2021 22:06:41 No.13719912 Report

Quoted By:

>>13719598
1/9 = 0.111...
+
8/9 = 0.888...
=
9/9 = 0.999...

Anonymous

Anonymous Tue 05 Oct 2021 22:21:37 No.13719987 Report

Quoted By:

>>13719898
>You seem to suffer from genuine mental retardation.
unnecesary rudeness.

Imagine somewhere there's a guy named John.
I tell you there's a guy named John in the other side of the country.
He's old and about to die.
I know no John, you say.
But I tell you he told me some key fact about your childhood that only you can know.
I tell you what he told me and it turns out that specific fact is indeed true.
You never met John, you never interacted with any John in you whole life. Does it mean John did never existed despite the fact he knows some specific information about you? you get it?

Ok, but what's the fact?
The fact is, my dear anon fren, is that you're a massive faggot and that $0.999\dots =1$

Anonymous

Anonymous Tue 05 Oct 2021 22:28:00 No.13720014 Report

Quoted By:

>>13719450
Filfthy mitts of a zoomer wrote this gay shit.

Anonymous

Anonymous Tue 05 Oct 2021 22:30:28 No.13720023 Report

Quoted By: >>13722236

>>13719803
does he actually explain how he gets here or how he justifies it?

Anonymous

Anonymous Tue 05 Oct 2021 22:47:07 No.13720072 Report

Quoted By: >>13720075

>>13719871
> I will not waste my time writing down huge amounts of them because it's stupid doing it"
If you actually, tried, you'd realise you'd get closer to 1, but never in fact reach it

Anonymous

Anonymous Tue 05 Oct 2021 22:47:58 No.13720075 Report

Quoted By: >>13720091 >>13720161

>>13720072
>but never in fact reach it
prove it

Anonymous

Anonymous Tue 05 Oct 2021 22:51:46 No.13720091 Report

Quoted By: >>13720093

>>13720075
each nine you add makes the error between your number and one diminish to a tenth of what it was (beginning from 1 if you start with "0."). ten to any negative power is a strictly positive number, hence none of the numbers you get by this process are exactly 1.

Anonymous

Anonymous Tue 05 Oct 2021 22:54:01 No.13720093 Report

Quoted By: >>13720099

>>13720091
And taking the step to the limit is what?

Anonymous

Anonymous Tue 05 Oct 2021 22:55:27 No.13720099 Report

Quoted By: >>13720102 >>13720158

>>13720093
a leap of faith

Anonymous

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Anonymous Tue 05 Oct 2021 22:56:08 No.13720102 Report

Quoted By: >>13720120

>>13720099
>a leap of faith

Anonymous

Anonymous Tue 05 Oct 2021 23:02:18 No.13720120 Report

Quoted By: >>13720124

>>13720102
sure, you can define ""a limit"" as is intuitive to you and the rules might work out very nicely, but turning a positive number to zero is an approximation.

Anonymous

Anonymous Tue 05 Oct 2021 23:05:01 No.13720124 Report

Quoted By: >>13720130

>>13720120
>but turning a positive number to zero is an approximation.
It's like saying you can never clean a surface completely because there always be an infinitesimal residual, you can only obtain an approximately clean surface.

You should learn to wipe your own ass before trying math.

Anonymous

Anonymous Tue 05 Oct 2021 23:07:05 No.13720130 Report

Quoted By: >>13721763

>>13720124
matter isn't infinitely divisible, you can (theoretically) get each and every particle of dirt out.

Anonymous

Anonymous Tue 05 Oct 2021 23:19:08 No.13720158 Report

Quoted By:

>>13720099
checked

Anonymous

Anonymous Tue 05 Oct 2021 23:21:20 No.13720161 Report

Quoted By: >>13720192

>>13720075
approximations are not equalities.
By claiming you can produce enough 9's to alchemy transmute it into a 1 is playing God.

We are but mere mortals

Anonymous

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Anonymous Tue 05 Oct 2021 23:40:16 No.13720192 Report

Quoted By:

>>13720161
>We are but mere mortals
Speak for yourself.

Anonymous

Anonymous Tue 05 Oct 2021 23:43:17 No.13720202 Report

Quoted By: >>13720203

what about 0.989999... ?

Anonymous

Anonymous Tue 05 Oct 2021 23:43:49 No.13720203 Report

Quoted By:

>>13720202
= 0.99
And?

Anonymous

Anonymous Wed 06 Oct 2021 04:49:53 No.13720908 Report

Quoted By:

>>13719456
That's it? That's your post? No cross-examination? No poiting to the flaws as to why it doesn't prove anything? I'm curious.

Anonymous

Anonymous Wed 06 Oct 2021 05:20:05 No.13720962 Report

Quoted By: >>13721399

$ 1 = \dfrac{3}{3} = 3 \cdot \dfrac{1}{3} = 3 \cdot 0.\bar{3} = 0.\bar{9} $

Anonymous

Anonymous Wed 06 Oct 2021 07:21:03 No.13721247 Report

Quoted By: >>13721377

>>13719450
X =.99999...
10X = 9.999999....
9X = 9
X=1

Anonymous

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Anonymous Wed 06 Oct 2021 07:31:41 No.13721263 Report

Quoted By: >>13721265

>ITT: mentally deficient midwits going in circles trying to prove something by assuming that which they're trying to prove.
People who can't grasp 0.999...=1 may be mathematically incompetent, but at least they have enough sense to see that they're being duped by teachers who don't understand what they're teaching.

Anonymous

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Anonymous Wed 06 Oct 2021 07:34:46 No.13721265 Report

Quoted By: >>13721282 >>13721377 >>13721409

>>13721263
projection, the post

Anonymous

Anonymous Wed 06 Oct 2021 07:37:54 No.13721268 Report

Quoted By:

$ \displaystyle (0.c_1 c_2 \dots) \cdot (0.d_1 d_2 \dots) = \sum_{n=1}^{ \infty} \dfrac{ \displaystyle \sum_{k=1}^{ \infty} c_n d_{k}}{10^n} $

Anonymous

Anonymous Wed 06 Oct 2021 07:45:42 No.13721282 Report

Quoted By: >>13721386

>>13721265
Go ahead and prove me wrong, tard. Where's your "proof"?

Anonymous

Anonymous Wed 06 Oct 2021 07:48:56 No.13721288 Report

Quoted By:

>infinity shows up again
u deserve to be 5150d for an 'infinite' amount of time

Anonymous

Anonymous Wed 06 Oct 2021 08:36:21 No.13721377 Report

Quoted By: >>13721399

>>13721247
this is a pretty good one, I think this was the one that convinced me as a kid. though personally nowadays I prefer a dedekind cut type of argument that (almost) foregoes infinities
>>13721265
show us the undeniable proof pls. if a midwit can shoot down your arguments, they can't be THAT great

Anonymous

Anonymous Wed 06 Oct 2021 08:41:32 No.13721386 Report

Quoted By: >>13721396

>>13721282
1/inf=0
after accepting that, it's just simple bookkeeping

Anonymous

Anonymous Wed 06 Oct 2021 08:47:15 No.13721396 Report

Quoted By: >>13721404

>>13721386
Do you understand what a proof is? No?

Anonymous

Anonymous Wed 06 Oct 2021 08:48:16 No.13721399 Report

Quoted By: >>13721403

>>13721377
>show us the undeniable proof
this is a nice short one >>13720962
loads of others exist oc:
https://en.wikipedia.org/wiki/0.999...#Analytic_proofs

Anonymous

Anonymous Wed 06 Oct 2021 08:49:20 No.13721403 Report

Quoted By: >>13721407

>>13721399
That one assumes what it's trying to prove.

Anonymous

Anonymous Wed 06 Oct 2021 08:50:17 No.13721404 Report

Quoted By: >>13721405

>>13721396
all the proofs I've seen are based on 1/inf=0

Anonymous

Anonymous Wed 06 Oct 2021 08:50:52 No.13721405 Report

Quoted By: >>13721409

>>13721404
So you don't understand what a proof is. Okay.

Anonymous

Anonymous Wed 06 Oct 2021 08:53:01 No.13721407 Report

Quoted By: >>13721411 >>13721835 >>13726161

>>13721403
nope, it's assuming 1/3=0.333..
good luck with disproving that

1/3 = 3/10 + 1/30
= 0.3 + 1/30
= 0.33 + 1/300
= 0.333 + 1/3000
:
= 0.3... + 1/inf
= 0.3... + 0
= 0.3...

Anonymous

Anonymous Wed 06 Oct 2021 08:54:03 No.13721409 Report

Quoted By:

>>13721405
>>13721265

Anonymous

Anonymous Wed 06 Oct 2021 08:54:24 No.13721411 Report

Quoted By: >>13721412

>>13721407
>it's assuming 1/3=0.333...
Which is based on the same concept being questioned in the first place.

Anonymous

Anonymous Wed 06 Oct 2021 08:55:35 No.13721412 Report

Quoted By: >>13721423

>>13721411
feel free to tell us what 1/3 is then

Anonymous

Anonymous Wed 06 Oct 2021 08:57:47 No.13721416 Report

Quoted By:

$ x= \frac{1}{10} \\ 0. \overline{9}=9x+9x^2+9x^3+9x^4+ \cdots \\ 0. \overline{9}=9x \left (1+x+x^2+x^3+ \cdots \right ) \\ 0. \overline{9}=(1-x) \left (1+\mathbf{x}+x^2+\mathbf{x^3}+x^4+ \cdots \right ) \\ 0. \overline{9}=1-x+ \mathbf{x-x^2}+x^2-x^3+ \mathbf{x^3-x^4}+x^4-x^5+ \cdots \\ 0. \overline{9}=1 $

Anonymous

Anonymous Wed 06 Oct 2021 09:00:09 No.13721423 Report

Quoted By: >>13721494

>>13721412
It is what it is, and you've not proven that the sum of an infinite series gives you the same thing. To prove that, you'd first have to prove that the sum of an infinite series should be a thing at all, which you can't really prove in any meaningful sense: anything you can possibly try is going to be a tautology, because mathematics proofs are tautologies in principle.

Anonymous

Anonymous Wed 06 Oct 2021 09:04:21 No.13721430 Report

Quoted By: >>13727041

>>13719762
I'm too lazy to verify this, but I believe that's because the (double precision) float's precision is limited to 17 significant digits. I assume python uses the IEEE 754 float by default.

https://en.m.wikipedia.org/wiki/Double-precision_floating-point_format

Anonymous

Anonymous Wed 06 Oct 2021 09:32:12 No.13721468 Report

Quoted By: >>13721478 >>13721480 >>13721485

Consider some decimal such $0.53647\dots$ . If we cut off a tail, for example the " $647...$ ", the information we're left with is that the original decimal lies somewhere in the interval $[0.53, 0.54]$ . It's an arbitrary choice to say that $0.53$ is a preferred approximation to the decimal, there's a continuum of other values which do it with the same precision. There's no apparent reason to prefer the lowest one possible.

$1.000\dots$ is the unique point on the number line which lies in every interval $[1,2], [1,\frac{1}{10}], [1,\frac{1}{100}]$ etc. because that's what you get with every subsequent rounding off.

$0.999\dots$ is the unique point on the number line which lies in every interval $[0,1], [\frac{9}{10},1], [\frac{99}{100},1]$ etc.

In the decimal representation, the "n-th digit" is derived from the LEFT endpoint of the n-th interval of the nested sequence by convention. The above nested sequences both have one endpoint fixed, and one approaching the fixed one. And it's only because of an arbitrary convention to prefer the LEFT endpoint as an approximation that one decimal looks static and the other one as an infinite process "which never gets there". Yes, the left endpoint of the nested sequence defining 0.999... never exactly equals 1. But you should be asking yourself why do you prefer this approximation of 0.999... in the first place. And why you have no problem with 1.000... being 1, even though the right endpoint of the defining nested sequences also never equals 1.

Anonymous

Anonymous Wed 06 Oct 2021 09:35:15 No.13721478 Report

Quoted By:

>>13721468
>[1,2],[1,110],[1,1100][1,2],[1,110],[1,1100]
$[1,2], [1,\frac{11}{10}], [1,\frac{101}{100}]$ *

Anonymous

Anonymous Wed 06 Oct 2021 09:36:41 No.13721480 Report

Quoted By:

>>13721468
>you should be asking yourself why do you prefer this approximation of 0.999... in the first place. And why you have no problem with 1.000... being 1
What if I think neither is 1?

Anonymous

Anonymous Wed 06 Oct 2021 09:38:33 No.13721485 Report

Quoted By:

>>13721468
most would surely prefer the approximation 0.54 for your initial example, as that's the closer endpoint that can be represented with the same number of digits. and for someone who believes 0.999...!=1, your second set of intervals would contain both 0.999... and 1, no?

Anonymous

Anonymous Wed 06 Oct 2021 09:41:59 No.13721494 Report

Quoted By: >>13721495

>>13721423
>you've not proven
i've proven it totally, assuming 1/3=0.333...
if you can't disprove that, then gtfo

Anonymous

Anonymous Wed 06 Oct 2021 09:42:44 No.13721495 Report

Quoted By: >>13721497

>>13721494
>assuming 1/3=0.333...
Why are you assuming what you need to prove? Anyway, yeah... mental deficiency.

Anonymous

Anonymous Wed 06 Oct 2021 09:43:35 No.13721497 Report

Quoted By: >>13721502 >>13721504

>>13721495
i'm proving 1=0.999...

try again

Anonymous

Anonymous Wed 06 Oct 2021 09:45:20 No.13721500 Report

Quoted By: >>13721507

>>13719450
Retards don't understand what sequences are, let alone series.
This is literally all there is to this dumb fucking debate that has been going on for years.

Anonymous

Anonymous Wed 06 Oct 2021 09:46:08 No.13721502 Report

Quoted By: >>13721509

>>13721497
You're basically stuck in a loop rephrasing the thing being questioned, because again, you're mentally deficient.

Anonymous

Anonymous Wed 06 Oct 2021 09:46:28 No.13721504 Report

Quoted By: >>13721512

>>13721497
you could skip the middle step by proving 1=0.999... by assuming that 1=0.999...

Anonymous

Anonymous Wed 06 Oct 2021 09:47:35 No.13721507 Report

Quoted By:

>>13721500
>years
try centuries

Anonymous

Anonymous Wed 06 Oct 2021 09:48:04 No.13721509 Report

Quoted By: >>13721513

>>13721502
1/3=0.333... is easy to accept, calculator agrees
1=0.999... is the weird one

if you don't accept 1/3=0.333...
that's your problem, not mine

Anonymous

Anonymous Wed 06 Oct 2021 09:49:17 No.13721512 Report

Quoted By:

>>13721504
calculator doesn't agree
has to be proved

Anonymous

Anonymous Wed 06 Oct 2021 09:49:40 No.13721513 Report

Quoted By: >>13721518 >>13721525

>>13721509
>1/3=0.333... is easy to accept
>1=0.999... is the weird one
It's the same concept in both cases, which you demonstrate when you try to "prove" one using the other. You're legit mentally deficient.

Anonymous

Anonymous Wed 06 Oct 2021 09:51:43 No.13721518 Report

Quoted By: >>13721526 >>13721537

>>13721513
lol
"if a then b" is perfectly logical
show 1/3 =/= 0.333...

Anonymous

Anonymous Wed 06 Oct 2021 09:53:09 No.13721525 Report

Quoted By:

>>13721513
>It's the same concept
calculator disagrees

Anonymous

Anonymous Wed 06 Oct 2021 09:53:33 No.13721526 Report

Quoted By: >>13721530 >>13721534

>>13721518
>my proof is: prove me wrong
Mentally deficient.

Anonymous

Anonymous Wed 06 Oct 2021 09:54:52 No.13721530 Report

Quoted By:

>>13721526
>didn't show 1/3 =/= 0.333...
lol

Anonymous

View Same Google iqdb SauceNAO ad hominem.jpg, 187KiB, 720x576

Anonymous Wed 06 Oct 2021 09:55:55 No.13721534 Report

Quoted By: >>13721555 >>13721557

>>13721526

Anonymous

Anonymous Wed 06 Oct 2021 09:57:20 No.13721537 Report

Quoted By: >>13721540

>>13721518
well, since 1!=0.999..., dividing by 3 we see that 1/3!=0.333...

Anonymous

Anonymous Wed 06 Oct 2021 09:58:41 No.13721540 Report

Quoted By: >>13721545

>>13721537
calculator disagrees
show the digit which isn't three

Anonymous

Anonymous Wed 06 Oct 2021 09:59:59 No.13721545 Report

Quoted By: >>13721553

>>13721540
the first one, it's a 0. are you even trying?

Anonymous

Anonymous Wed 06 Oct 2021 10:00:41 No.13721547 Report

Quoted By:

$ \displaystyle \sum_{n=1}^{\infty}\frac{9}{10^n} = \frac{9}{10} + \frac{9}{100} +\frac{9}{1000} + ... = b = \frac{1}{10}(9 + \frac{9}{10} + \frac{9}{100} +...) = \frac{1}{10}(9+b) = b \\ \frac{1}{10}(9+b) = b \\ \frac{9}{10} = \frac{9}{10}b \\ 1 = b $

Anonymous

Anonymous Wed 06 Oct 2021 10:01:50 No.13721552 Report

Quoted By:

>>13719891
AH

Anonymous

Anonymous Wed 06 Oct 2021 10:01:52 No.13721553 Report

Quoted By: >>13721556

>>13721545
that's your proof?
lol

Anonymous

Anonymous Wed 06 Oct 2021 10:02:51 No.13721555 Report

Quoted By: >>13721557 >>13721563

>>13721534
>be a smug nu-atheist midwit with zero intellectual accomplishments
>be forced to count insults as evidence for your superior intellect

Anonymous

Anonymous Wed 06 Oct 2021 10:03:31 No.13721556 Report

Quoted By: >>13721562

>>13721553
what? it's my proof that there's a non-3 digit that you asked for.
my actual proof relies on my calculator saying that 0.999...!=1, so it's exactly the same principle as yours.

Anonymous

Anonymous Wed 06 Oct 2021 10:04:27 No.13721557 Report

Quoted By: >>13721563

>>13721555
>>13721534

Anonymous

Anonymous Wed 06 Oct 2021 10:06:18 No.13721562 Report

Quoted By:

>>13721556
>>13721556
so they're all 3, ok

Anonymous

Anonymous Wed 06 Oct 2021 10:06:49 No.13721563 Report

Quoted By: >>13721570

>>13721555
>>13721557

Anonymous

Anonymous Wed 06 Oct 2021 10:09:35 No.13721570 Report

Quoted By: >>13721582

>>13721563
they never show the non-3 decimal, just start doing schizo shitposting...
lol

Anonymous

Anonymous Wed 06 Oct 2021 10:12:23 No.13721576 Report

Quoted By:

$x=0.999...$
$10x=9.999...$
$10x=9+0.999...$
$10x=9+x$
$9x=9$
$x=1$
$0.999...=1$

Anonymous

Anonymous Wed 06 Oct 2021 10:14:46 No.13721582 Report

Quoted By: >>13721597

>>13721570
my calculator gives "0.3333333432674408" when input 1/3, so there's your non-3 decimals.

Anonymous

Anonymous Wed 06 Oct 2021 10:19:53 No.13721597 Report

Quoted By: >>13721607

>>13721582
get a better one
https://www.google.com/search?hl=en&q=1%2F3

Anonymous

Anonymous Wed 06 Oct 2021 10:22:07 No.13721607 Report

Quoted By: >>13721835

>>13721597
that's obviously wrong, it gives a different result??

Anonymous

View Same Google iqdb SauceNAO 1632479321809.jpg, 238KiB, 676x1024

Anonymous Wed 06 Oct 2021 10:58:06 No.13721695 Report

Quoted By:

>imagine thinking .999... is real
>imagine thinking it is equivalent to an infinite series
>imagine thinking this abominable heresy is equivalent to the whole
i would pity your foolishness if you didn't disgust me with your arrogance

Anonymous

Anonymous Wed 06 Oct 2021 11:30:15 No.13721763 Report

Quoted By: >>13721779 >>13721827

>>13720130
are primes real

Anonymous

Anonymous Wed 06 Oct 2021 11:40:13 No.13721779 Report

Quoted By:

>>13721763
no they're natural

Anonymous

Anonymous Wed 06 Oct 2021 11:56:38 No.13721810 Report

Quoted By:

>6/2 =3
>6= 2*3
>Checks out

>1/3 =3.333
>1= 3*3.33333
>?

Its just an anomaly of base 10. It'd probably be even in base 9 or 12.

Anonymous

Anonymous Wed 06 Oct 2021 12:11:37 No.13721827 Report

Quoted By:

>>13721763
numbers aren't "real", they're just a model

Anonymous

Anonymous Wed 06 Oct 2021 12:18:51 No.13721835 Report

Quoted By:

>>13721607
>>13721407

Anonymous

Anonymous Wed 06 Oct 2021 13:09:17 No.13721935 Report

Quoted By: >>13722870

>>13719509
Imagine actually thinking knowledge/practice is equal to intelligence. Anyone who isn't a retard could learn that proof you posted. The fact of the matter is that many people haven't put the time into it because they haven't needed to.

Anonymous

Anonymous Wed 06 Oct 2021 15:15:45 No.13722229 Report

Quoted By: >>13726657

>>13719459
$0.9 = 1 - 0.1$
$0.99 = 1 - 0.01$
...
$0.999...9 = 1 - (0.1)^n$ where there are $n$ 9's to the right of the decimal place.
As $n\to \infty$ , $(0.1)^n \to 0$ , hence $0.\bar{9} = 1$ .

Anonymous

Anonymous Wed 06 Oct 2021 15:18:56 No.13722236 Report

Quoted By: >>13722672

>>13720023
It's a matter of the definition of convergence of a series. You can find everything you need in your basic analysis textbook.

Anonymous

Anonymous Wed 06 Oct 2021 17:51:41 No.13722672 Report

Quoted By: >>13722770 >>13722887

>>13722236
no, I meant him specifically. the dude is pretty strictly against infinite and infinitely precise things.

Anonymous

Anonymous Wed 06 Oct 2021 18:33:48 No.13722770 Report

Quoted By: >>13723735 >>13724624 >>13725588

>>13722672
Believe it or not, $0.\bar9$ is not infinitely precise

Anonymous

Anonymous Wed 06 Oct 2021 18:35:47 No.13722775 Report

Quoted By:

>>13719459
Meds. Now.

Anonymous

Anonymous Wed 06 Oct 2021 19:28:34 No.13722870 Report

Quoted By:

>>13721935
>I can do it but I've just never tried but i for sure know that i can do it cause reasons

Yeah you belong here

Anonymous

Anonymous Wed 06 Oct 2021 19:30:52 No.13722876 Report

Quoted By:

>>13719465
Why choose $N=\log_{10}\frac{1}{\epsilon}+1$ instead of $N=\log_{10}\frac{1}{\epsilon}$ ? Is it to express the largeness of N?

Anonymous

Anonymous Wed 06 Oct 2021 19:36:59 No.13722887 Report

Quoted By: >>13724624 >>13725637

>>13722672
$0.\bar{9}$ is just formal notation for the limit of the series $a_n = 1 - (0.1)^n$ , $n=1,2,3,...$ . The limit just happens to be 1. Likewise $a_n \to x$ as $n\to \infty$ is just formalism as well. Everything having to do with infinite decimals is just formalism for convergent series. The series or the limits themselves do not require infinity or "infinite preciseness." It's a matter of the definition of convergence.

Anonymous

Anonymous Wed 06 Oct 2021 21:12:53 No.13723046 Report

Quoted By: >>13723133

>>13719450
your proof assumes the thing you're trying to prove...

Anonymous

Anonymous Wed 06 Oct 2021 21:48:32 No.13723133 Report

Quoted By:

>>13723046
It doesn't.

Anonymous

Anonymous Thu 07 Oct 2021 02:35:06 No.13723735 Report

Quoted By: >>13723884

>>13722770
>let's pretend finite is infinite
wrong
it's infinitely precise

Anonymous

Anonymous Thu 07 Oct 2021 03:54:34 No.13723884 Report

Quoted By: >>13723890

>>13723735
And yet Wildberger doesn't seem to think so

Anonymous

Anonymous Thu 07 Oct 2021 03:57:11 No.13723890 Report

Quoted By: >>13724861

>>13723884
>Wildberger
lol

Anonymous

Anonymous Thu 07 Oct 2021 05:00:14 No.13723967 Report

Quoted By: >>13724046 >>13724868

Its interesting that over and over people independently come up with the idea that .999...?1. I think its because, even if people aren't aware of it, there's a rigorous way one can construct a system where the two numbers are different. It ultimately comes down to crafting a non-zero number such that $\varepsilon < \frac{1}{n} \forall n \in \mathbb{N}$ . Within the usual real numbers, such a small number can't exist, so we are forced to assign .999.. and 1 to the same value, since there difference cannot be anything other than 0. It turns out that if you take any statement which holds for every finite natural number (in this case, the family of statements are 1 ?.9, 1?.99, 1?.999, etc.), its possible to construct a system where the statement holds for all natural numbers (in this case, a system where it holds that 1?.9999...). The idea is called compactification (iirc, I don't quite remember the name of the theorem).

Anonymous

Anonymous Thu 07 Oct 2021 05:40:22 No.13724046 Report

Quoted By: >>13724770

>>13723967
3 < ?
3.1 < ?
3.14 < ?
3.141 < ?
3.1415 < ?
3.14159 < ?
3.141592 < ?
3.1415926 < ?
3.14159265 < ?
this continues endlessly
? < ?

your fields medal is in the mail

Anonymous

Anonymous Thu 07 Oct 2021 11:46:50 No.13724624 Report

Quoted By: >>13725648

>>13722770
elaborate? do you mean that it's just 1, or that you think it corresponds to some finite number below that? or that it's just an object that's somewhere there but has no precise value?
>>13722887
sure, I was just wondering how wildberger copes about it. his takes are sometimes interesting.

Anonymous

Anonymous Thu 07 Oct 2021 12:44:31 No.13724770 Report

Quoted By: >>13725009

>>13724046
you're assuming that 3.14159265.. = pi. you have to do it like this:

0.9 < 0.999...
0.99 < 0.999...
0.999 < 0.999...
this continues endlessly and there is no reason to assume that it stops being true
0.999... < 0.999...

Anonymous

Anonymous Thu 07 Oct 2021 13:23:28 No.13724861 Report

Quoted By:

>>13723890
Remember that God created the concept of numbers.
Satan created the concept of collecting several numbers together, thus allowing
them to become indecent with one another.
Wildberger is fighting the good fight. Do not take his name in vain.

Anonymous

Anonymous Thu 07 Oct 2021 13:25:59 No.13724868 Report

Quoted By:

>>13723967
If you are thinking of Robinson arithmetic and hyperreals, then .999... and 1 are still the same:
https://en.wikipedia.org/wiki/Hyperreal

Anonymous

Anonymous Thu 07 Oct 2021 14:06:36 No.13725009 Report

Quoted By:

>>13724770
someone give this genius two medals

Anonymous

Anonymous Thu 07 Oct 2021 17:03:28 No.13725588 Report

Quoted By: >>13725598

>>13722770
Aren't you aware of significant figures? Of laboratory measurements?

Anonymous

Anonymous Thu 07 Oct 2021 17:05:20 No.13725598 Report

Quoted By: >>13725608

>>13725588
what do significant figures have to do with 0.999... being 1?

Anonymous

Anonymous Thu 07 Oct 2021 17:07:14 No.13725608 Report

Quoted By:

>>13725598
Fixing a finite number of significant figures there's not infinite decimals at all and for example $1$ is quite different from $1.00$ .

Anonymous

Anonymous Thu 07 Oct 2021 17:12:59 No.13725637 Report

Quoted By:

>>13722887
Wilberger have no problem with reapeating decimals per se. He just wonders why arithmetic with reapeating decimals is so difficult and different from arithmetic with the corresponding $\frac{a}{b}$ fractions.
See pic attached in the post: >>13719803

Anonymous

Anonymous Thu 07 Oct 2021 17:15:05 No.13725648 Report

Quoted By: >>13726569

>>13724624
Wilberger has no problem with reapeating decimals per se. He just wonders why arithmetic with reapeating decimals is so difficult and different from arithmetic with the corresponding $\frac{a}{b}$ fractions.
See pic attached in the post: >>13719803

Anonymous

Anonymous Thu 07 Oct 2021 17:15:26 No.13725651 Report

Quoted By: >>13725673

the 0.999... = 1 believe they are houdini, slipping a 0.0...1 up their sleeve and hiding it in the ... portion of the notation.

They arn't fooling anyone

Anonymous

Anonymous Thu 07 Oct 2021 17:18:31 No.13725673 Report

Quoted By: >>13726234

>>13719450
>>13725651
Is the notation $0.\bar{9}$ any less ambiguous than the $0.999\ldots$ for you?

Anonymous

Anonymous Thu 07 Oct 2021 19:02:26 No.13726080 Report

Quoted By: >>13726161 >>13726637

>>13719632
WTF Bro? This is like a circular proof. you are using 1/3 = 0.333...

Anonymous

Anonymous Thu 07 Oct 2021 19:03:33 No.13726086 Report

Quoted By:

>>13719450
stop rounding, absolute midwit

Anonymous

Anonymous Thu 07 Oct 2021 19:21:23 No.13726161 Report

Quoted By:

>>13726080
>>13721407

Anonymous

Anonymous Thu 07 Oct 2021 19:40:03 No.13726234 Report

Quoted By:

>>13725673
But the difference betwixt the lefte and right sleeve

Anonymous

Anonymous Thu 07 Oct 2021 21:08:47 No.13726569 Report

Quoted By:

>>13725648
ah right, thanks. I guess this should be evident from the pic.

Anonymous

Anonymous Thu 07 Oct 2021 21:27:04 No.13726637 Report

Quoted By:

>>13726080
circular reasoning kills the schizo

Anonymous

Anonymous Thu 07 Oct 2021 21:32:05 No.13726657 Report

Quoted By:

>>13722229
>converges
>equals
retard

Anonymous

Anonymous Thu 07 Oct 2021 21:59:52 No.13726733 Report

Quoted By: >>13726755 >>13726869

>>13719450
>mathematicians seriously think that 0.9999999...=1 but won't accept that 1/0=infinity, something so patently obvious that any sixth grader with an undertanding of 0, infinity, and division would tell you it's true.
why are mathematicians so retarded?

Anonymous

Anonymous Thu 07 Oct 2021 22:08:53 No.13726755 Report

Quoted By: >>13726810

>>13726733
Your sixth grader, who knows more than any mathematician ever knew, also knows that 1/-0 = -infinity, right?

Anonymous

Anonymous Thu 07 Oct 2021 22:30:26 No.13726810 Report

Quoted By: >>13726890

>>13726755
It's not that the sixth-grader is smarter, it's that he hasn't yet been indoctrinated to believe that division by 0 is impossible.
There are definitely peculiarities to division by 0, but they are not insurmountable. You might use a signless infinity, or a signed 0.
Either way, x/0=infinity is supported by the fact that
x*0=0 , therefore 0=0/x and x=0/0
As dividing by 0 yields infinity, 0/0 is the same as 0*infinity, meaning:
x=0*infinity , therefore x/0=infinity and x/infinity=0
If that doesn't convince you, consider a finite segment of the number line. The length of this segment could be any non-zero real number X. The segment is made up of an infinite amount of dimensionless (length=0) points, which when added together (0*infinity) add up to the length of the line segment (X).

Anonymous

View Same Google iqdb SauceNAO divideby0.png, 76KiB, 1498x1153

Anonymous Thu 07 Oct 2021 22:49:52 No.13726869 Report

Quoted By: >>13726974 >>13727147

>>13726733
infinity or -infinity?

Anonymous

Anonymous Thu 07 Oct 2021 22:54:47 No.13726890 Report

Quoted By:

>>13726810
Good luck with passing sixth grade anyway.
Maybe hire a fourth grader as a tutor who will explain stuff to you.

Anonymous

Anonymous Thu 07 Oct 2021 23:24:18 No.13726974 Report

Quoted By: >>13728165

>>13726869
Both, just as the square root of 4 is both +2and -2

Anonymous

Anonymous Thu 07 Oct 2021 23:47:48 No.13727041 Report

Quoted By:

>>13721430
can confirm.

t. numerical anal major

Anonymous

Anonymous Fri 08 Oct 2021 00:35:53 No.13727147 Report

Quoted By:

>>13726869
Unsigned infinity

Anonymous

Anonymous Fri 08 Oct 2021 05:55:18 No.13728019 Report

Quoted By:

>>13719520
that’s literally what that means though

Anonymous

Anonymous Fri 08 Oct 2021 07:05:45 No.13728165 Report

Quoted By: >>13728194 >>13729134

>>13726974
>square root of 4 is both +2and -2
nope
$ \sqrt {x^2} \ne \pm x, \quad \sqrt {x^2} = \left | x \right | $

Anonymous

Anonymous Fri 08 Oct 2021 07:18:01 No.13728194 Report

Quoted By:

>>13728165
you have literally agreed with him

Anonymous

Anonymous Fri 08 Oct 2021 07:33:23 No.13728228 Report

Quoted By:

>>13719450
How to get from line 6 to 7? Am retarted

Anonymous

Anonymous Fri 08 Oct 2021 15:33:11 No.13729134 Report

Quoted By:

>>13728165
While the radical sign, by convention, does only result in a single, "principal" square root, that doesn't change the fact that there numbers also have an equivalent but negative square root.
Regardless, if it's valid to take an operation that has two results with an equal absolute value and just take that absolute value as the "correct" result, then it should also be valid to take the absolute of both positive and negative infinity as the answer to x/0.

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