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/sci/ - Science & Math

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7681901 No.7681901[DELETED]  [Reply] [Original]

It's time for a math paradox:
0.99999999...=1

>> No.7681905

In order for it to be a paradox, two contradictory things must be true. All I see is one true thing.

>> No.7681916

>>7681901
What's the paradox?

>> No.7681930

>>7681916
In a technical sense it's not a paradox ( my bad) but I thought it was interesting and I wanted to post it

>> No.7681943

>>7681901
Huuuuuh, pray tell where the paradox is? I'm kinda confused here

>> No.7681981

>>7681905
>>7681916
>>7681943
Well, it's actually a paradox because while it APPEARS true, 0.999999... is not equal to 1. They are very close and may SEEM to be equal, but it is a trivial proof to show they are indeed not equal

>> No.7682005

>>7681981
No, it is a "trivial" proof to show that they are indeed equal.
Did you skip first term anon?

>> No.7682039
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7682039

>>7681981
>but it is a trivial proof to show they are indeed not equal
Actually it's the other way around. It's trivial to prove that they ARE equal.

>> No.7682047

>>7681981
1/3 = 0.333...
0.333... * 3 = 0.999...
1 = 0.999

>> No.7682061

0.99...=x
9.99...=10x
9.99...-0.99...=9x
9=9x
1=x

Boom.

>> No.7682066

>>7682047
>>7682061
I would like to point out that these proofs are actually non-strict and rigorless.
There is nothing to say these particular infinite series work this way at all.
Yes 0.9... is equal to 1, but these are not the correct way to go about proving them.

>> No.7682071

>>7682066
I'm not extremely well versed in the maths; care to post a proper explanation (if it's within reason)?

>> No.7682072

>>7682066
He is correct. One musy actually use the rigorously proved properties of series to demonstrate equality.

>> No.7682092

>>7682071
>>7682072
These are not correct because we cannot place a universal assumption on infinite series.
Any good mathematics course will teach you that when it comes to infinite series (and on a digression, infinite integrals), to keep our notation and definitions consistent, we need to give well-defined definitions to them.
In fact, even with these consistent notations and definitions, we still get "funny" results (see the Riemann rearrangement theorem).
A quick google search on invalid arguments for 0.9 equals 1 should satisfy you.
An example of such a discussion appears here:
https://en.wikipedia.org/wiki/Talk:0.999.../Arguments#Explanation_erroneous_proving_digit_manipulation_.28moved_from_talk.29
(be warned that not everything here is correct)

>> No.7682188

>>7682005
[math] \displaystyle
1 = \frac {3}{3} = 3 \cdot \frac {1}{3} = 3 \cdot 0.333... = 0.999...
[/math]

>> No.7682512

A while ago I explained a similar "paradox". Short version:
Inventor invents a sort of matrix machine.
10 seconds of using the machine is 100 years inside the virtual reality.
Every user will complete their life goal inside the virtual reality and every time they use the machine although their virtual lives may vary.
If the inventor uses the machine his goal will be to invent and use the machine inside the machine. Witnesses will see him wake in 10s but he will continue to copy himself and make more machines and go deeper and deeper etc, personally never waking up.
Very similar to
.9999999...=/=1
Or
.333333333...=/=1/3

>> No.7682514

As for why this happens:
Calculators are wrong. Calculators simply have no idea what infinity is and if they did they would not be able to output the answer. Its how computers work. Humans understand infinity as an IDEA.
1 ÷ 3 = 0.33333 [calc] the threes are the calculator trying to cut apart the thirds from each other
1 ÷ 3 = 1/3 [brain] understands that each third is sperate from one another and that we can evenly cut a circle in thirds.

>> No.7682534

Here's a real paradox:
>>7682512 is the most retarded poster on /sci/
>>7682514 is more retarded than >>7682512

>> No.7682544

>>7682188
What are you getting at? Why is this at my post?

>> No.7682576

>>7682544
example of trivial proof

>> No.7682603

>>7682512
oh dearie, little baby’s first zeno paradox

>> No.7682604

>>7682188
You're assuming 1/3=0.333333 which it doesn't

>> No.7682693

>>7682604
Lrn2cdot fgt pls

>> No.7682729

>>7682604
oh I'm pretty confident, but please,

do feel free to prove it wrong

>> No.7682756

Traditional decimal definitions mean the number represents 9/10 + 9/100 + 9/1000 + ....
This is the geometric series [math]\sum_{n=1}^{\infty} \frac{9}{10^n} = 9*/frac{1}{10-1} = 1[/math]

If you wish to invent new definitions for existing mathematical syntax go ahead.

>> No.7683483

>>7682576
>>7682693
You realise that proof is NOT mathematically rigorous in any way right?
It's not a trivial proof when it lacks rigor.

>> No.7683491

>billionth troll repost

why is this garbage still up?

>> No.7683498

>>7683483
It's a perfectly good proof
as long as 1/3=0.333...

If you can't believe that
disprove it or shut up.

>> No.7683502

>>7683498
What you start off with is as ridiculous as what you end up with.
This 0.333... business is nothing but shorthand. Imprecise shorthand at that.
We cannot perform any analysis on it whatsoever.
One possible representation of 1/3 involves geometric series as many others have posted.
Those make analytic sense.
0.333... on the other hand is garbage jargon and very open to abuse.
Compare this to using Leibniz notation for differentials.
Rather than paraphrasing what is already around I'll link:
http://math.stackexchange.com/questions/335560/is-1-divided-by-3-equal-to-0-333
Google around and convince yourself that 0.333... really is garbage.

>> No.7683644
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7683644

>> No.7683654

>>7683498
Here's how you disprove it. if it's true, then 0.9999999...=1 which it isn't.
6/10 made me reply

>> No.7683655

>>7683491
It is a classic.

>> No.7683700

>>7682756
>posting the actual proof
>nobody's paying attention because the thread is full of shites
just leave them to their doom

>> No.7684089

>>7683654

ohhh, so mathematically rigorous
yes you are a new Hilbert no doubt

>> No.7684097

>>7683502
0.333... is shorthand for
[math]
\displaystyle \sum _ {n=1} ^ \infty \frac {3}{10^n}
[/math]

nothing imprecise about that

>> No.7684101

>>7684097
This. Argue this faggot.

>> No.7684103

>>7684097
Did you actually take onboard the entire post?
Since my reply to you here would just be the same post.
What is your current level of mathematical understanding? Perhaps I can cater to your level to help you understand.
The "proof" with 0.333... given is typically what is shown to "middle schoolers".

>> No.7684112

>>7684103
blah blah blah

still haven't seen a proof that
1/3 isn't 0.333...

>> No.7684116

>>7684112
I very strongly urge you to review your notes for the first term of your mathematics course if you're finding topics like this an issue.

>> No.7684118

>>7684116
>still haven't seen a proof that
>1/3 isn't 0.333...

>> No.7684128

>>7684112

let x = 0.9999999....
[math]10x = 9.99999...[/math]
[math]10x-x = 9.9999... - 0.999999...[/math]
[math]9x = 9[/math]
[math]x = 1[/math]


Therefore,
[math]1 = 0.9999...[/math]

>> No.7684135

>>7684118
There exists a theorem saying: Given p/q, it is possible to represent p/q in base b, if and only if, b contains all the prime factors of q.
A paper that is of interest can be found here:
http://www.liafa.jussieu.fr/~cf/publications/AFSwords05.pdf

>> No.7684136

>>7684118
what kind of shit course are you on, this is analysis I stuff

>> No.7684137

Proof by contradiction:

Assume that
[math]0.999... \ne 1[/math]
That would mean that [math]1 - 0.999 \ne 0[/math]
It'd be of value: [math]0.000...1[/math]
But the [math]0.000...[/math] denotes that the zeros go on forever. If you have the trailing 1 at the end, there exists a point where there's an end to the zeros, meaning they don't go on forever. The very number is impossible.

>> No.7684144

>>7684136
still not proving
that 1/3 isn't 0.333...

>> No.7684149

>>7681901
0.99999 can never equal 1 because 1 is 1 and 0.99999 is 0.99999

>> No.7684150

>>7684144
Have you tried dividing 1 by 3 using long division?
No matter how many 3s you get, you'll get that trailing remainder forever. It's a recursive property. Do it by hand and see for yourself.

>> No.7684153

>>7684149
[math]0.99999 \ne 0.999...[/math]
But [math]0.999... = 1[/math], those are one and the same, and there's plenty of proof. Just look at >>7684128 and >>7682188

>> No.7684154

>>7684150
yeah, that my point

>> No.7684156

>>7684144
Are you looking for some sort of algebraic proof?
Do you understand that proofs do not need to be algebraic?
The material that has been linked in this thread is sufficient to help you understand this.
Honestly, what is your level of understanding in mathematics? Middleschool? Highscool? Which year of uni? Postgrad?
It's very difficult to know what I can assume when explaining this to you, and without knowing this it will just end up being a waste of explanation for other posters trying to assist you too.

>> No.7684157

>>7684154

Woops, I'm drunk. Nevermind, you're the worng person.

>> No.7684159

>>7684144
Define what you think a proof is for us please.

>> No.7684166

>>7684156
>ad hominem bs

cough up the proof already

>> No.7684169

>>7684166
There is no intended ad hominem, apologies if it seems that way.
The proof needs to fit your level of understanding.
Read over the links provided before, but apparently you're not understanding these.
Hence why I'm asking for your mathematical competency.
Answer that and a proof that you're likely to understand can be given.

>> No.7684170

>>7684159
I have no idea, surprise me

adhd barking as in >>7684156
certainly isn't enough

>> No.7684172

>>7684170
He's right though, there are a lot of proofs on this topic.
I don't really understand why you're refusing to answer these questions.
If you're afraid of the banhammer, just say you're 50 with highschool understanding or something.

>> No.7684178

>>7684170

If it helps, check this out.
https://math.berkeley.edu/~hutching/teach/proofs.pdf

I can assure you, though, it's been algebreically proven that 0.999... = 1. I think there's a proof by contradiction in here too.

>> No.7684181

An intuitive understanding is that writing 1/3 as a rational is different from writing it as a real number. Real numbers are defined using sequences of rationals and one consequence is that .333...=1. http://math.stackexchange.com/questions/11/is-0-999999999-1/60#60
This has a more rigorous explanation of what I said.

>> No.7684209

>>7684181
.333...=1/3

>> No.7684404

>>7684178
sigh.
>>7682188
>>7683498
>>7684097
>>7684112
>>7684118
>>7684144
>>7684166
>>7684170
is from me, so I need no convincing

yell at the other guy

>> No.7684440

>>7683654

https://en.wikipedia.org/wiki/0.999......

Stop mistaking your retardation for knowledge!