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/sci/ - Science & Math

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6212418 No.6212418 [Reply] [Original]

So there seem to be quite a few /sci/borgs who deny the identity 1 = 0.999....
Quick inquiry for you esteemed individuals:
in your estimation, what percentage of mathematicians agree with you in your skepticism?

(Let's stipulate that a 'mathematician' is someone with a mathematics degree from an accredited college or university).

>> No.6212420

>muh populum

>> No.6212424

>>6212418
Prolly zero.

>inb4 appeal to authority fallacy

These fuckers study maths for a living. If something as basic and trivial as 0.999...≠1 would you think they wouldnt have realized it by now? "Hurr I took high school math infinitesimals don rely exist I'm smrter than all mathematishins XD"

>> No.6212429

the series converges to 1, trivially

make another shit thread now

>> No.6212436

>>6212424
>>inb4 appeal to authority fallacy

(Let's stipulate that a 'mathematician' is someone with a mathematics degree from an accredited college or university).(OP)

>> No.6212455

>>6212418
Less than 1%.
Don't give no fucks.

>> No.6212460

>It converges to 1 at infinity
I just can't see why people accept this

>> No.6212513

Seriously, how can people be so dense?

0.999... = 1. What mathematicians think should have no bearing, it's just a fact. This shouldn't even be discussed. Why is /sci/ so shit?

>> No.6212521

>>6212513
0.999… + 1 = 1.999…

>> No.6212524

>>6212460
Because it's a provable statement that follows from simple assumptions which everybody agrees on.

>> No.6212529

>>6212418
decimal places are important in displaying additional information about a number.

both answers are correct and are showing the same number at different decimal places.

>1/10, wouldn't respond again.

>> No.6212534

>>6212521
Also known as 2.

>> No.6212538

>>6212418
>So there seem to be quite a few /sci/borgs who deny the identity 1 = 0.999....
/pol/ and /b/ leak from time to time, that's about it.

>> No.6212548

No one in the entire fucking world who has taken more than 1 or 2 years of uni maths thinks 1 and .999... are different. Particularly those working in analysis.

If I ever meet an analysist who makes that mistake I'll give my entire life savings to charity. Cos it won't happen

>> No.6212554

>>6212418
The problem is <span class="math">\underline{IT~CANNOT~BE~PROVED!}[/spoiler]

>> No.6212558

>>6212554
It's been proven multiple times, in multiple ways. Also, "be proven," not "be proved."

>> No.6212564

.999 does not equal 1....
the same as 999 does not equal 1000

>> No.6212565

>>6212564
0.999... is not the same as 0.999, m8. The nines repeat ad infinitum.

>> No.6212570

>>6212558
Retard

All those "proofs" presuppose that 1=.999... and thus are invalid. To do any sort of arithmetic/operations with any given real number requires you to assume it first.

In fact, it is ludicrous for 2 different element of a set to be shown to be equal in the first place.

>> No.6212572

>>6212570
1/9 = 0.111... (by calculator)
Multiply both sides by 9.
1=0.999...

A proof with no presuppositions.

>> No.6212577

>>6212570
The correct proof doesn't do any arithmetic with 0.999.... Even if it did, making arithmetic operation with it only assumes it's a real number, it doesn't assume it's equal to 1. And the whole point of the proof is that they are not different elements of the set, but the same element written in two different ways, just like 1/2 and 2/4 are the same number.

Why am I even replying to such an obvious troll?

>> No.6212580

>>6212572
>approximation by calculator
>proof
Engineer?

>> No.6212582

>>6212572
>assuming the generality of algebra
>2013

Somewhere out there Cauchy is rolling in his grave

>> No.6212584

>>6212580
Any single digit number divided by 9 will equal that number repeated to infinity. No approximations.

>> No.6212588

>>6212582
>infinite series

>> No.6212590

>>6212584
>Any single digit number divided by 9 will equal that number repeated to infinity.
Correct
>No approximations.
Wrong. Your calculator approximates 1/9 by 0.111111111111111 or some other finite number of 1's after the 0. That doesn't constitute a proof it's just an approximation.

>> No.6212592

>>6212590
Because it can't fit infinite 1's on the screen, m8. It can do the operation ad infinitum, but can't fit it on the screen.

>> No.6212596

>>6212592
are you retarded?

>> No.6212597

>>6212596
Nope.

>> No.6212598

>>6212592
Exactly, it can't, that's why it's no good for proving shit like this. If I ask my pocket calculator the square root of 2 it gives me 1.4142135, and if I square that number on the same calculator, it gives me 2 again. Does that mean 1.4142135 is the square root of 2? No, a quick trip to a scientific calculator will tell me that 1.4142135^2 = 1,99999982358225 which is quite a long way away from 2 as far as a proof that it was the square root of 2 is concerned.

>> No.6212601
File: 36 KB, 480x320, At least read a baby level math book before claiming you know mathematics.jpg [View same] [iqdb] [saucenao] [google]
6212601

>>6212577
>just like 1/2 and 2/4 are the same number

They are clearly not the same and there is no way of proving they are without assuming they're the same in the beginning. You can't just derive or prove an equivalence relation when something break but must clearly state that one is in effect and prove that any operations done on any arbitrary chosen label is well founded <span class="math">before[/spoiler] doing anything else.

>>6212584
>>6212588

You're doing operations on an infinite object with the only justification of "it works for all finite objects". Fail.

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

>> No.6212604

OP here.
Before this thread gets any more derailed let me reiterate the question I'm interested in:
>in your estimation, what percentage of mathematicians agree with you in your skepticism?
(2 anons have responded so far).

At the moment I'm not interested in convincing anybody of anything, just trying to gauge people's mentalities.

Of course on the other hand feel free to, ya know, shit all over this thread if you so desire.

>> No.6212603

>>6212598
Which means shouldn't take the number 1.4142135. You should just use sqrt(2), unless you put "..." after the former number, implicitly meaning there's infinity more digits after.

>> No.6212605

>>6212592
You calculator can store an infinite amount of digits? So it has infinite RAM, that must have been pricey, and infinitely large is size, holy shit that means I am part of your calculator, my whole world is a lie.
Not the other anon, but I too will inquire, are you retarded?

>> No.6212606

>>6212604
Pretty much everyone's going to say 0 to practically 0, OP. This isn't an opinion poll, just facts.

>> No.6212610

>>6212606
I'd like to confirm though.

>> No.6212608

>>6212605
I didn't say store.

>> No.6212612

>>6212601
>They are clearly not the same and there is no way of proving they are without assuming they're the same in the beginning
No shit sherlock. You fucking define them precisely so that they end up being the same. That doesn't change the fact that under the conventional definition they are provably the same, just like under the conventional definition 0.999... and 1 are provably the same.

Holy shit, you're retarded and you're still a fucking arrogant prick.

>> No.6212615

>>6212612
>provably the same

>Assume p
>Therefore p

Not a proof

>> No.6212613

>>6212570
>In fact, it is ludicrous for 2 different element of a set to be shown to be equal in the first place.
And we're the ones assuming our result before proving them?

>> No.6212617

>>6212603
Yes, and your calculator is incapable of putting that "..." therefore no good for the proof you want.

>> No.6212621

>>6212613
> x≠y & x=y
>logical

>> No.6212619

>>6212513
Most of /sci/ are high school students... And they aren't even good students...

>> No.6212620

>>6212615
No, no, no. We assume only some axioms, then we define an object (the real numbers defined through decimal expansion), then using those axioms we prove that under this definition 0.999...=1. Of course our initial assumptions imply 0.999...=1, or else we would never be able to prove it in the first place. By your reasoning nothing in mathematics is a proof because it's all implied by axioms we assume.

>> No.6212623

>>6212620
>we define an object (the real numbers defined through decimal expansion)

>https://en.wikipedia.org/wiki/.999...#Infinite_decimal_representation
>This construction can too be rigorously shown to satisfy all of the real axioms after defining an equivalence relation over the set that defines 1 =eq 0.999...

>then using those axioms we prove that under this definition 0.999...=1.

Yeah, not a proof.

>> No.6212628

>>6212623
If Wikipedia chose to start by defining 0.999...=1 that's okay. Some people choose to start defining the real numbers by their properties as if they were axioms and it doesn't change a thing, others start by ZFC and build their way up from there all the way up to real numbers.

Turns out you can build all of the real number system from sets of axioms which do not include 0.999...=1 and still deduce that equality. Turns out that's also the conventional way to do it.

>> No.6212631

>>6212623
>Commonly in secondary schools' mathematics education, the real numbers are constructed by defining a number using an integer followed by a radix point and an infinite sequence written out as a string to represent the fractional part of any given real number
>using baby's first naive definition of a real number
>At least read a baby level math book before claiming you know mathematics.jpg
Oh, god my sides. You blew it there m8.

>> No.6212640

>>6212628
>Some people choose to start defining the real numbers by their properties as if they were axioms and it doesn't change a thing

Not rigorous

>start by ZFC and build their way up from there all the way up to real numbers.

That's what the Wikipedia article did.

>Turns out you can build all of the real number system from sets of axioms which do not include 0.999...=1 and still deduce that equality

No you can not. Claiming it works with cuts or sequences or whatever presupposes that decimals bijectively map to them which presupposes the decimals satisfy the real axioms which REQUIRES 0.999... to be defined to be 1. Circular argument.

>> No.6212642

>>6212631
>naive definition of a real number
>naive

It's just as rigorous as construction by cuts or completion of the rationals.

>> No.6212644

>>6212640
>REQUIRES 0.999... to be defined to be 1
No, it requires 0.999... to be defined as the limit to a series just like any other infinite decimal expansion, and it turns out that under this definition it is provable under ZFC that it equals one. I'm not replying to you anymore, you're either a troll or a retard.

>> No.6212658

>>6212644
>to be defined as the limit to a series just like any other infinite decimal expansion

But the reals <span class="math">\bf{DO~NOT~EXIST~YET}[/spoiler] so you can not define a limit to them and assume completeness.

All you could prove doing that to a different construction is that the map of decimals strings to it is not bijective to whatever construction you want for the "reals".

>> No.6212666

>>6212658
>All you could prove doing that to a different construction is that the map of decimals strings to it is not bijective to whatever construction you want for the "reals".
That's pretty much it, yeah. Any reasonable construction for the reals is not bijective with the decimal expansions. That's why the decimal expansion construction is naive and that's why in the conventional constructions 0.999...=1 is a theorem and not a definition.

>> No.6212670
File: 789 KB, 641x639, 1386562490857.png [View same] [iqdb] [saucenao] [google]
6212670

>zero

If you deny it then tell me what is 1-0.999.... ?

>inb5 0.0001 (...means there are infinitly many nines nigger)

>> No.6212697

>>6212666
>naive

It's nothing of the sort. Are fractions a naive construction of the rationals? People (in particular high school math teachers who failed at being real mathematicians) are retarded and leave out mentioning (or don't even know) that the set is modulated by an equivalence relation and instead try to "prove" it.

Lack of rigor and relaying on intuition are the enemies of all Mathematicians.

>> No.6212744
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6212744

Well it was worth a try.

>> No.6212764

if 1 does not equal .999...
then 1/3 does not equal .333...

>> No.6212802

(not op)
I have also heard of negative orders. Is this possible or is it entirely hypothetical? If possible, what materials react in a such way?

>> No.6212806

>>6212802
my computer farted, wrong thread

>> No.6212921

>>6212764
Well it doesn't. It's a bad approximation. Use fractions if you want to stay exact. Decimals cannot express 1/3.

>> No.6212922

>>6212921
Except they can...that's why we use repeating fractions.

>> No.6212929

>>6212617
Nope, the point is 1.4142135.... and \sqrt{2} both represent the same real number, or the ``same element of the set'', if you insist.
Just like 0.9999.... and 1 represent the same number. Or 2 and 100/50.

>> No.6213533

>>6212929
1.4142135.... is not a well-defined expression because it doesn't repeat. You CANNOT represent square root of 2 as a decimal number.

>> No.6213545

>>6212418
>who deny the identity 1 = 0.999....
How about you fuck off back to /b/ with your tired old trolling?

>> No.6213761

Daily reminder to filter all .999... threads

>> No.6214400

99.999...% of all mathematicians agree with me. The percentage of mathematicians disagreeing with me is infinitesimally small but unfortunately not zero.

>> No.6214405

is 0.999...998=0.999...?
if so then all numbers are equal
if such a number: 0.9...98 doesn't exist, well then neither does 0.999...

>> No.6214438

>>6214405
You put an end in it by placing an 8 in the end of the nines. If it really have infinite nines them it never reachs an end and therefore never reach that 8.

>> No.6215238

>>6214438
But the 8 is still there irregardless of whether it will ever be reached.

>> No.6215334

>>6215238
It's not, that's the meaning of infinity.

There is no end.

see
>>6214666

>> No.6216835

>>6215334
That thread doesn't exist anymore. Can you post the link here?

>> No.6219385

The equals sign is to be read as approximately equals.

>> No.6219465

>>6216835
Yeah, it's in the /sci/ guide.

https://imageshack.us/a/img40/4547/1314137966992.png

>> No.6219751

>>6212644
>it turns out
Professor Mcdonald, is that you?

>> No.6219865

True. .999... = 1 BUT only if we are using the real number system. The reasoning behind this? We create the reals with basic assumptions, math needs to start somewhere. For the reals, this includes the assumption that the only way 2 numbers can be separate, different elements, is if there is a number in between them. Is there a real number between .999... and 1? No, because the nines in .999... repeat forever and there is never any room for a number to fit between then and .999... and 1. Infinity is also a concept described in the real number system, and the way it is described allows .999 to equal 1. It's just the assumptions that were made at the beginning of the real number system that leads us to say that, for the reals, .999... = 1.

>> No.6220172

>>6212418
I thinks its true in math, but in real life application it would make no sense ?

>> No.6221472

>>6219751
No.

>> No.6221511

>>6220172
That's because infinity doesn't exist in real life

>> No.6221531

Hey, what fraction equals .9 repeated?

>> No.6221540

>>6221531
1/1

>> No.6221588

>>6221531
9/9

>> No.6222782

>>6221540
>>6221588
But those evaluate to 1 and not to a repeating decimal.

>> No.6222882

>>6222782
Time to quote wikipedia.

>Some real numbers have two infinite decimal representations. For example, the number 1 may be equally represented by 1.000... as by 0.999...

>Conventionally, the version with zero digits is preferred; by omitting the infinite sequence of zero digits

Both have a repeating decimal, we just choose to not to use it, and both are the same thing.

>> No.6223719

>1 = 3/3
>1 = 1/3 + 1/3 + 1/3
>1 = .3333 +.333333 + .33333333333333333
>1 = .999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

It's seriously that simple

>> No.6223742

OP, the way the real numbers are defined make it true using our system of logic.
You can claim anything you want but there are a set number of axioms used to define real numbers and a set procedure to represent real numbers using decimal representation. Also, there are set axioms for natural numbers and their representation.

to define a real number using decimals you have to either define it as an explicit summation of natural numbers multiplied by a power of 10 (also a natural number) then it would be written as
n.a1,a2,a3,a4 where n and ai are natural numbers, this would represent
n + a1 * 10^(-1) + a2 * 10^(-2) etc.

That is just how decimals are defined. there are other ways to define decimals implicitly such as 0.111... which is really just abuse of notation since it really just means the summation to infinity where all ai's are the natural number 1.

If you want to write 0.9999...9999 as a finite number of 9s then yes they are different numbers but writing 0.9999... is not a decimal it is a recipe for a decimal representation of some real number. there is no property saying that decimal representation is unique and the whole basis of the converse argument is unjustified.
if you want to use some other definition for decimal representation then go for it, your claim will be right but you will also lose a lot of valuable deductions made in real analysis

>> No.6223774

I'd say somewhere between 0 and (1-0.999...)%

>> No.6223797

This is why "scientists" should learn math properly, via proofs and theorems, rather than plug and chug calculus a-la Stewart.
It's as if none of you science folk know anything about deductive logic.

>> No.6223807

I would say 99.99...% of qualified mathematicians understand that 1 = 0.999...

>> No.6223814

Which is bigger?
0.9... or 0.99...

>> No.6224220

1 =/= .999 ...

1.) 1 + 1 =/= 1 + .999...
2.) 1 = 1
3.) 1 + .999 ... = 1.999 ...
4.) Therefore, 1.): 11 =/= .999 ...

>> No.6224229

>>6224220
No shit that 11 =/= 0.9...

However 1.0...+ 1.0... = 2.0... = 1.9...

>> No.6224246

>>6223807
Kek

>> No.6224245
File: 59 KB, 500x512, 1386988931791.jpg [View same] [iqdb] [saucenao] [google]
6224245

>> No.6224627

>>6224220
n = 1.999...
10n = 19.999...
9n = 18.0
n = 2
1 + 1 = 2
1.999... = n = 2
1 + 1 = 1.999...

>> No.6224629

>>6223814
they're the same because 0.9... means 0.99... means 0.999... and 0.999999999999999...
>full retard
my jimmies are rustled

>> No.6225121

>>6224627

2 =/= 1.999 ...

>> No.6225130

>>6224627
9n=17.999

>> No.6226122

>>6225130
Do I have to solve for n?

>> No.6226165

>>6225121
Nope.
They are the same too.
10.999... = 11.000...
5.999... = 6.000...
159.999... = 160.000...

>> No.6227398

>>6226165
Bascially, what your saying is you can approximate every number by other numbers very close from below?

>> No.6227406

>>6227398
Those aren't approximations, those are numbers with two different representations, one that has infinite 9 and one that has infinite 0.
It doesn't work for numbers such as 1.333... or any other besides .999... and .000...

>> No.6227411

>>6227406
>any other besides .999... and .000..
that ends in .999... and .000...

>> No.6228148
File: 33 KB, 916x408, 1387144325545.jpg [View same] [iqdb] [saucenao] [google]
6228148

>> No.6228517

>>6227411
But 9 =/= 0

>> No.6228592

>>6228517
Yes, but what we are talking about is a number which is represented by infinite 9s and infinite 0s.

>> No.6229255

>>6228592
No such number exists.

>> No.6229480

>>6229255
Their decimal expansion is represented by infinite 9s and infinite 0s.
Are you happy now?

>> No.6230930

>>6229480
No fraction can generate an infinite sequence of 9s.

>> No.6231041

>>6230930
1/1 for example.

Which can be represented as 1.000... (one with infinite 0s)
Or 0.999... (0 with infinite 9s).

The whole point is that those represent the exact same number, so when it can either be represented as 0.999... or 1.000..., and we just choose 1.000... normally instead of 0.999...

>> No.6231226

0.999... = 1

1 - 0.999... = 0.000... = 0
1 - 0 = 1
=> 0.999... = 1

QED

>> No.6231235

99.999...% of mathematicians agree that 0.999... = 1;

>> No.6231251

>>6225130
10n - n = 19.999... - 1.999...
9n = 18

although 17.999... does in fact equal 18.0 I suspect you are either trolling or going full retard

>> No.6231257

>>6230930
If no fraction can give an infinite sequence of 9s then does it matter if 1 = 0.999...?

>> No.6231475

>>6231257
<span class="math"> \frac {9}{9} = \frac {1}{9} \cdot 9 = 0.999...[/spoiler]

>> No.6231481

>>6212534
Shut your mouth

>> No.6231895

>>6231475
That's incorrect math. 9/9 = 1

>> No.6231945

>>6231895
<span class="math">
1 = \frac {9}{9} = \frac {1}{9} \cdot 9 = 0.999...
[/spoiler]

>> No.6231949

>>6231945
don't bother trying man... last time one if these threads started i had to try and explain listable and non-listable infinities to the plebs... it's just not worth it

>> No.6231951

>>6212564
.999 doesn't equal 1, there is a 0.001 difference.
Good job!

>> No.6231967

Proof via intuition.
154 = 154
Therefore removing the second and third number should yield equality e.g

154 - 54 = 154 - 54
100 = 100

Therefore, when dealing with identical values we see that preceding numbers can be ignored and still return an equal sum

1.0000... = 0.999.....
1.000... -000... = 0.999....-0.999....
1 =/= 0

Therefore 0.999..... =/= 1

>> No.6231974

>>6231967
nope, therefore
<span class="math">
0.999... \ne 0
[/spoiler]

>> No.6232389

>>6231951
>completely missing the point of this thread
>not understanding recurring figures after a decimal point
0.999 doesn't equal 1, but 0.999... (recurring) does equal 1

>> No.6232393 [DELETED] 

>>6231967
you can't subtract .000,,, on one side and 0.999,,, on the other, that implies 0.999 = 0.000 which it doesn't

>> No.6232398

>>6212418
I think for every 10,000 math PhDs there will be one fedorafag who doesn't accept 0.999... = 1 despite all the proof

>> No.6232404

>>6231967
you can't subtract .000,,, on one side and 0.999,,, on the other, that implies 0.999... = 0.000... which it doesn't.
1.000... = 0.999...
1.000 - 0.000... = 0.999... - 0.000...
1.000... = 0.999...

>> No.6232421

>>6231967
>subtracting by 0 on one side and .9999... on the other

>> No.6232946

If 0.99... = 1
Then 2* 0.99... = 1.99...8 = 2
??

>> No.6232982

>>6212524
It's wrong, though. 0.99999... doesn't converge because it's not a series, it's "shorthand" for <span class="math">\lim_{n \rightarrow \infty} \sum_{k=1}^{n} 9 \times 10^{-k}[/spoiler], not a number.

>> No.6232987

>>6212418
0.999... is an impossible number.

>> No.6232988

>>6212697
>Lack of rigor and relaying on intuition are the enemies of all Mathematicians.
Fuck off Hilbert wannabe, you're still retarded and can't math

>> No.6233020

>>6212524
So is 1+1=2

>> No.6233029

>>6232398

There's really no "proof," it's essentially a fucking definition.

Repeating decimals are defined to be limits of sequences of partial sums.

>> No.6233077

>>6232946
you never get to the 8, because infinity

>> No.6233154

>>6231967

this has to be the most amazingly fucked up troll proofs I have seen on sci

>> No.6233199

>>6233077
But 0.9+0.9 = 1.8
0.99+0.99 = 1.98
I'm sure you see where I'd be going with this

>> No.6233216

>>6233199

Where you're going is that you don't actually understand the notation.

Repeating decimals are /defined/ to be limits of sequences. Not every scribble you put on a piece of paper is meaningful; when you write ".9999...8," that doesn't actually /mean/ anything. It is incompatible with the definition for that notation.

>> No.6233222

>>6231895
see
>>6222882

>> No.6234077

>>6233216
Then how do you explain what I wrote? Where does that (supposedly meaningless) 0.0...1 go?

>> No.6234226

>>6234077
please just let this thread die, im really sick of seeing it, i dont goddamn care if you believe 1=0.999... or not.

>> No.6234240

>>6234226
Give me an answer, then.

>> No.6234547

>>6234240
He just said it, there is no 0.0...1.
That's simply not how infinity works.

Let me quote wikipedia again:
>Some students interpret "0.999..." (or similar notation) as a large but finite string of 9s, possibly with a variable, unspecified length. If they accept an infinite string of nines, they may still expect a last 9 "at infinity".[35]
ie, there isn't a 0.999...9, and there isn't a 0.0...1.

>> No.6234885

>>6234547
>He just said it, there is no 0.0...1.

I acknowledged that with
>(supposedly meaningless)

But it still doesn't answer my question.

>> No.6234903

>>6212429
Its not. You're using the formula which omits the crucial infinitesimal part.
read the disproval of 1=0.999... and the section on proof debunking
http://pastebin.com/0x35eiWn

>> No.6234936

>>6234903
>oh look 1=/= 0.999... in my obscure useless number system
You should assume we are dealing only with the reals.

>> No.6234962

>>6234885
4/3 = 1.333... = 0.999... + 0.333...

>> No.6235944

>>6234962
That assumes 0.99... = 1,

>> No.6235947

One third times three equals one. There is no end to infinity.

>> No.6236262

>>6235944
It's just another use of his logic.

0.9 + 0.3 = 1.2
0.99 + 0.33 = 1.32
As you can see if this process goes to infinity, there will never be a 2, thus 1.333... = 0.999... + 0.333...

>> No.6236490

>>6236262
>there will never be a 2
>every step contains one
Math logic

>> No.6236494

>>6236490
infinity - 1 = infinity
Infinity logic.

>> No.6236505

1 - .1 = .9

1 - .01 = .99

etc.

1 - .000 ... 1 = .999...

but .000 .. 1 implies infinite zeros, so is equal to zero.

Therefore:

1 - 0 = .999 = 1

>> No.6236542

>>6212604
About (1 - 0.999...)%

>> No.6236545

>>6236505
0 = 0.0...1 = 0.0...2 = 0.0..3 = 0.999... = 1
0 = 1

>> No.6236549

>>6236545
Again, the notation 0.0...1
0.0...x
Has absolutely no meaning.

There isn't a number "at infinity".

>> No.6236551

>>6236549
1.0*10^inf > 0.99..*10^inf

>> No.6236552

>>6213533
You cannot, I can.

>> No.6236557

>>6236551
>infinity > infinity
Nope.

>> No.6236558

>>6236551

I don't think so, bub.

>> No.6236572

>>6236557
>>6236558
>muh magic limits
gbk2highskl

>> No.6236576

>>6236572
0.1*10^inf = 1*10^inf
infinity = infinity

>> No.6236587

>>6236576
infinity =/= infinity/infinity

>> No.6236593

>>6236587
infinity/infinity is indeterminate
Same as infinity - infinity.

Not sure what you are trying to say there.

>> No.6236597

0.11111..=1/9 0.222222..=2/9 -> 0.8888888..=8/9 0.999999..=9/9=1
its as easy as that.

>> No.6236605

0.24 = 1/4
0.48 = 1/2
0.72 = 3/4
0.96 = 4/4

1 = 4/4 = 0.96

1 = 0.96

>> No.6236606

>>6236605
0/10

>> No.6236621

given 10x = .99999....
thus 1x = .09999...
thus 9x = .9
thus x = .1
multiply by 10 on both sides
10x = 1
thus .99999... = 10x = 1

Not that fucking hard, you don't need a sloppy 1/3 proof. That said, I'd guess about 99% of mathematicians agree on this. Some are just a bit too into metaphysics...

>> No.6236624

Infinitesimals exist, you'll all see!

>> No.6236639

>>6236621
10x = 9.9
1x = 0.99
9x = 9 - 0.9
x = 1 - 0.1
1 - 0.1 =/= 0.99

>> No.6236685

>>6236639
He defined 10x = 0.999..., not 10x = 9.999...

>> No.6236695

>>6236685
10x = 0.999
1x = 0.099
9x = 9 - 0.099
x = 1 - 0.01
1 - 0.01 =/= 0.999

>> No.6236711

>>6236695
9x= 0.999... - 0.0999...
x = 0.111... - 0.0111...
x = 0.1
10 x = 1

>> No.6236775

>>6236711

9x = 0.9 - 0
x = 0.1 - 0/9
10x = 1 -( 0/9)10

>> No.6236802

>>6236775
>x = 0.1 - 0/9
x = 0.1 - 0
10x = 1 - 0 = 1

>> No.6236807

>>6212418

A statistical approximation of the number of people holding a degree in mathematics from an accredited college or university who agree that 1 != 0.9 repeating.

This thread is a troll.

>> No.6236814

>>6234077

It doesn't "go" anywhere, that's simply not a valid manipulation.

>> No.6236819

>>6212529
No, that would mean they're different because you'd lose precision.

>> No.6236821

0.999... doesn't exist. It isn't a real number.

>> No.6236823

>>6236821
Is 0.333... not a real number too?

>> No.6236826

>>6212418

.999... isn't real. It's like saying apples = oranges and defining oranges to be .999... apples. You can't have .999 apples so why are you comparing apples and oranges?

>> No.6236827

>>6236823
It isn't. Infinity doesn't exist.

>> No.6236832

>>6232987
When you move your hand from one point in space to another, you travel a distance of 1.. let's call it gibbies. So to get from 0 gibbies to 1 gibbies, you have to go through all gibbies in between. This includes 0.55555 gibbies..., so why not also 0.99999 gibbies?

>> No.6236835

>>6236826
No, it's more like saying 1 apple = 1 apple.

>> No.6236847

>>6236827
>>6236823
>>6236821
>In mathematics, the repeating decimal 0.999... (sometimes written with more or fewer 9s before the final ellipsis, or as 0.9, 0.(9), or 0.9 with dot over the 9) denotes a real number that can be shown to be the number one. In other words, the symbols "0.999..." and "1" represent the same number.
>denotes a real number
Looks real to me.

>> No.6236852

>>6236847
you missed mine:
>>6236832

>> No.6236853

>>6236847

God is real.
.999... is real.

See how easy that was? I just proved God is real.

>> No.6236859

>>6236852
>>6236853
bad troll. goodbye

>> No.6236860
File: 125 KB, 1296x973, 1387483371590.png [View same] [iqdb] [saucenao] [google]
6236860

>>6236853
>trying to argue with wikipedia
top lel

>> No.6236864

>>6236859

Mad I'm using logic to win arguments. gtfo

>> No.6236869
File: 90 KB, 491x397, 1387483565976.gif [View same] [iqdb] [saucenao] [google]
6236869

>>6236864
trolley

>> No.6236870

>>6236832
>infinitesimals
Nope, we are on the reals here.
That means your infinitely small distance from one point to another doesn't exist, therefore they are the same.

>> No.6236873

>>6236832
0.99999 sure, but not 0.99999...

>> No.6236875

>>6236870
You're missing context
>>6236873
Try harder still

>> No.6236876

>>6236875
>Try harder still
I'm not trolling. Stop being an idiot.

>> No.6236878
File: 2 KB, 32x32, 1387484027031.png [View same] [iqdb] [saucenao] [google]
6236878

>>6236876
oh, sorry, I was confused

>> No.6236879

Suppose 0.999... = 1= 1.000...

Ten 9 = 0, contradiction. QED

>> No.6236881

>>6236878
>32x32

>> No.6236884

>>6236879
>Ten 9 = 0, contradiction. QED
Come back when you can form mathematical sentences.

>> No.6236887

>>6236875
And you are missing understanding of math.

>> No.6236889
File: 830 B, 16x16, 1387484387458.png [View same] [iqdb] [saucenao] [google]
6236889

>>6236881
my bad

>> No.6236891
File: 2 KB, 32x32, 1387484483113.png [View same] [iqdb] [saucenao] [google]
6236891

>>6236879

>> No.6236895

>>6236889
>16x16

>> No.6236897
File: 1 KB, 22x22, 1387484661361.png [View same] [iqdb] [saucenao] [google]
6236897

>>6236895

>> No.6236901

>>6236826
>You can't have 1/3 of an orange
>You can't have a negative orange
>You can't have an imaginary orange
>You can't have things that behave as particles and as waves
Back to middl-, actually never mind that, just start again from the beginning.

>> No.6236907

0.9 + 0.1 = 1
0.99 + 0.01 = 1
0.999 + 0.001 = 1

So

0.999...+ 0.000...1 = 1

But 0.000...1 =/= 0, so we have a contradiction. QED

>> No.6236913

>>6236907
>0.000...1
Stop with that.
That number doesn't exist.

It's 0.
There is no 1 at the end, it's literally impossible, there is no end, it is infinite.

>> No.6236914

>>6236913
>I don't understand math

>> No.6236915

>>6236913
Except that's wrong.

>> No.6236920

Why do any of you even care about this topic. It seems fairly irrelevant.

>> No.6236921

>>6236914
>>6236915
>Doesn't understand the reals

>If they accept an infinite string of nines, they may still expect a last 9 "at infinity".

>> No.6236935

Our smallest unit of measurement is a Planck time.

0.999... x Planck time = Time for light to travel 1 Planck unit.

So even on the smallest unit of measurement that exists, 0.999... still equals One unit.

>> No.6236975

>>6236913
>Who is Cantor

>> No.6236995

>>6236975
Somebody who probably isn't alive, and isn't mentioned in any high school.
Therefore doesn't matter.

>> No.6237233

>>6236995
Cantor is mentioned in every high school math book.

>> No.6237300

<span class="math">\[\lim_{x\rightarrow \infty }\sum_{k=0}^{x}(.9*10^{i}) = 1\][/spoiler]

>> No.6237391

>>6236915

We're going to dispense with the shitty notation (who the fuck uses repeating decimals, anyway?) and deal purely with the concepts here:

Definition: We call a number e "infinitesimal" if for all natural numbers n we have e < 1/n.

Claim: There exists no infinitesimal real number.

Proof:

Without loss of generality, we consider only positive real numbers.

Let E be the set of positive infinitesimal real numbers. By way of contradiction, assume E is nonempty.

Then clearly E is bounded above. By the completeness axiom, E must have a supremum. Let x = sup(E).

If x is infinitesimal, then it holds that x < 1/n for any natural number n. It thus follows also that 2x < 1/n for any natural number n. This is a contradiction, since then 2x would be an element of E greater than sup(E).

If x is not infinitesimal, then there exists some natural number n such that 1/n =< x. But then 1/2n would be an upper bound of E less than x, which is also a contradiction.

Thus, our assumption is false, and the set of infinitesimal real numbers is empty.

Now shut the fuck up and stop pretending to know math.

>> No.6237392

>>6234903
>Step 9: multiply both sides by infinity
hue

>> No.6237401

>>6237391
>expecting someone who thinks .999... != 1 to know the axioms of the real line.

Haha.

>> No.6237415

>>6237391

Your claim should have been "there exists no nonzero infinitesimal real number."

Otherwise, this is correct.

>> No.6237431

There should be some sort of fundamental rule that you are not allowed to use the word "infinity" if you have not taken an analysis course.

>> No.6237432

>>6235944
<span class="math">
1 = \frac {9}{9} = 9 \cdot \frac {1}{9} = 9 \cdot 0.111... = 0.999...
[/spoiler]

>> No.6237437

>>6237432

"Proofs" like this completely miss the point.

The reason this is true is because of the definition of a repeating decimal, not because of some semi-intuitive manipulations of other things which "look right."

Attempting to "prove" it this way is little more than an appeal to the fact that people who claim otherwise often accept that ".111 = 1/9," which isn't a "proof" of the claim, it's a proof that the doubter's beliefs about the real numbers are inconsistent.

>> No.6237444

>>6237391
>Claim: There exists no infinitesimal real number.
Why would that matter?

You might as well be proving that there exists no infinitesimal rational or natural number.

Infinitesimals belong in other meaningful sets, like the hyperreal or surreal numbers.

Are you seriously so ignorant that you reject any set of numbers they didn't teach you about in grade school?

>> No.6237447

>>6237437
>'point' in a pointless discussion..... lel

>> No.6237448

>>6237444

No one who claims ".999... != 1" is talking about hyperreal numbers, because you don't denote hyperreal numbers with decimals. Decimal notation implies a real number.

I doubt anyone who has claimed the contrary position in this thread knows what a model is, or what the transfer principle is, or has any formal math experience at all.

>> No.6237456

>>6237437
In <span class="math">
1 = \frac {9}{9} = 9 \cdot \frac {1}{9} = 9 \cdot 0.111... = 0.999...
[/spoiler] there are four equal signs. Since you seem to object, which equal sign fails, #1, #2, #3 or #4?

>> No.6237460

>>6237456
He said the 1/9=.111...
so the third one

>> No.6237467

>>6237456

What you wrote is trivially true, but does not address the core point of confusion for someone who thinks ".999... != 1."

Such a person could resolve the inconsistency revealed by that "proof" by simply expanding their claim to deny that "1/9 = .111..." is true, and they'd still be wrong but that argument would no longer help.

>> No.6237469

>>6237460
Really? Ok, you tell me the answer to 1/9.

>> No.6237476

>>6237467
there are people who accept 1/3=0.333... but not 0.999...=1

>> No.6237477

>>6237437
>The reason this is true is because of the definition of a repeating decimal
But it's not true.

0.999... = 1 "looks right" to some people and "looks wrong" to other people, but any proper definition of a repeating decimal will simply disallow repeating nines in the set of rational numbers, because the sane convention is to allow only one decimal expansion of each rational number. Nobody ever uses 0.999... to mean 1, except in arguments that 0.999... supposedly is equal to 1. 0.999... is a violation of convention, and therefore not a rational number at all.

Therefore, if you're using repeating nines, and you're expressing numbers with a sane convention, you're not in the set of rational (or real) numbers, and repeating nines should have a distinct meaning. The obvious interpretation is that you'd use it to express a value with an infinitesimal component.

The conventions of math are built on reasoning like this. 0.999... is either not a number, or it's an expression of a value from a set with infinitesimals. Either way, it's not a proper way to express a real or rational number.

>> No.6237478

>>6237476

Yes, there are. Those people may not end up drawing the conclusion you want them to draw when you present them with that argument, because all you're doing is pointing out the inconsistency in their beliefs rather than explaining why it is true that .999... = 1.

>> No.6237480

>>6237477
The convention on decimals is to allow every terminating decimal to have an equal non terminating representation, and to favour the former while not disallowing the other.

>> No.6237483

>>6237477
>but any proper definition of a repeating decimal will simply disallow repeating nines in the set of rational numbers, because the sane convention is to allow only one decimal expansion of each rational number.

I don't know where you've studied math, but I've not met a single person who does serious research in Analysis who'd agree with this.

Most of them don't use repeating decimals at all, because it's a shitty notation, but when they do the standard definition is /always/ in terms of limits of sequences of partial sums.

No one /ever/ uses repeating decimals to denote infinitesimals in the field of hyperreals. There's no clean way one would do so.

".999..." is poor notation for "a real number equal to one."

>> No.6237489

>>6237477
>The conventions of math are built on reasoning like this.
No the conventions of maths are built on simplicity and consistency.

Decimals are a sum, infinite decimals an infinite sum. Not "a sum except when it's all 9s, then it's not a number at all."

>> No.6237490

>>6237489

Thank god, someone who actually knows math.

>> No.6237497

>>6237489
>the conventions of maths are built on simplicity and consistency.
Yes, having two decimal expansions of the same number for some, but not all rational numbers sure is simpler and more consistent than having only one for every rational.

>> No.6237506

>>6237497

Yes, it is.

You're making it extremely clear that you're not actually a mathematician. As standard notation means what people in the field agree that it means, not what you personally want it to mean, your opinion is irrelevant.

>> No.6237507

>>6237497
Here the simplicity is minimizing the amount of assuptions, the clunky "except when it's all 9s" is the culprit.

>> No.6237513

>>6232982
define 0.999..., then, without using series

>> No.6237515

>>6237497
Yes it is. Because to have one representation for all you have to inconsistently disallow the summation of some representations, for no real reason other than it seems neat. And as it will vary in different bases, it is also somewhat arbitrary. Constructing an equivalence class in the decimals and having them represent the reals is way more elegant.

>> No.6237516

>>6237506
Okay, tell you what, you submit a paper with 0.999... written in place of 1, with no comment and no special reason, just using it as if it were equivalent, and see if they don't insist on you correcting it before it's published.

Repeating nines are NOT conventional, and a lot of math on decimal expansions assumes there is one and only one expansion of each real number.

Sometimes, someone might write a definition down which would allow repeating nines. I submit that this is intellectually lazy, inconsistent with convention, and basically incorrect.

>> No.6237521

>>6237516
>a lot of math on decimal expansions assumes there is one and only one expansion of each real number.

[citation needed]

>> No.6237525

>>6237516
That is different from the point you were making. The convention is to use 1, but you are claiming the convention is also to not allow 0.999... to equal 1.

Try publishing a paper claiming that.

>> No.6237527

>>6237516
>a lot of math on decimal expansions assumes there is one and only one expansion of each real number.
No, math never assumes this as it is completely wrong. Math states that terminating decimals also have a non terminating equivalent.

How old/educated are you, by the way?

>> No.6238622

>>6237391
>assume E is nonempty.
nope

>> No.6238650

>>6237527
>Math states that terminating decimals also have a non terminating equivalent.
Okay. What's the non-terminating equivalent decimal expansion of 0?

>> No.6239018

>>6238650
Would it not be 0.000... ?
Although I honestly have no idea if it would be

>> No.6240366

9.999.... is VERY close to 1. Mathematicians just call them equal for practical purposes.

>> No.6240396

>>6240366
Nope, they represent the exact same number, as infinitesimals don't exist, see
>>6237391

>> No.6240834

>>6240396
>infinitesimals don't exist
I think Newton would disagree.

check and m8

>> No.6241001

>>6240834
>appeal to authority
Nope, go ahead and disprove it.

Infinitesimals do not exist on the reals.

>> No.6241506

>>6241001
Is zero an infinitesimal?

>> No.6241612

suppose that 1 != 0.999..., then 1-0.999 != 0. so there exists n > 0 such that 1-0.999...= n. this n would then have the property of being the smallest possible positive number. now conider 1/n, since n is the smallest positive number, 1/n is the largest positive number. but 1+1/n >1/n. Thus there is a contradiction so 1 = 0.999...

>> No.6242153 [DELETED] 

>>6241612
nope <span class="math">\infty +1 = \infty[/spoiler]

>> No.6242162

>>6241612
>this n would then have the property of being the smallest possible positive number.
Pulling this definition out of your ass? There is no reason to claim this. There could be infinite infinitesimals.

>> No.6242288

>>6242162
There are, but it's the smallest of them.

>> No.6242294

>>6241612
>but 1+1/n >1/n
How is this a contradiction?

>> No.6242328

>>6212418
0

>> No.6242344

>>6242328
Wrong, 0.0...01

>> No.6242348

>>6242288

There is no such thing as the smallest infinitesimal, as they decrease INFINITELY. just like there is no largest possible number.

>> No.6242351

>>6242288
ITT: high schoolers argue by pulling concepts out of their ass: "if we take the number at the end of the infinite sequence and treat it like a real number"

>> No.6242353

>>6242351
This describes all of /sci/
place aalcri

>> No.6242356

>>6242294
... with muh feelings of course

>> No.6242360

>>6236552
do it then im waiting

in fact, i'll always be waiting

>> No.6242361

>>6232988
not that guy but why is being a hilbert wannabe a bad thing

>> No.6243178
File: 111 KB, 501x571, 1387758093921.jpg [View same] [iqdb] [saucenao] [google]
6243178

>1/9 * 9 = 9/9 = 1
>1/9 * 9 = 0,111... * 9 = 0,999...
>1 = 0,999...
>qed

oh wow, that was hard

>> No.6243183

>>6243178
9/9 and 0,999... aren't the same

>> No.6243191

>>6212418
Convergence, limits, et cetera are not the same as something being something exactly.

They are called limits for a reason.

Infinitesimals are rigorously defined. Accept them and move on.

>> No.6243225

>>6243183
Yes, they are.

>every real number has a
unique infinite decimal in Δ representing it; but, in addition, rational numbers
of the form p/q (not necessarily in 'lowest terms') with q a power of 10 have a
second representation (outside Δ) by an infinite decimal terminating in 9's.

>> No.6243233

>>6243191
And on the reals they are exactly the same.

1 - 0.9... = 0

>> No.6243396

I'm one of the mathematicians who would disagree with skepticism.

0.9999... = 9/10 + 9/100 + 9/1000 + ....
= 9/10(1 + 1/10 + 1/100 +....)
= 9/10(1/(1 - 1/10)) = 9/10(1/(9/10)) = 9/10(10/9) = 1.
Simple analysis

>> No.6243406

>>6243396
>= 9/10(1/(1 - 1/10))
Whoa, slow down there, speed racer.

>> No.6243437

Suppose 0.999... and 1 are distinct real numbers. Then there exists another distinct real number greater than 0.999... and less than 1. Clearly this is not the case, so they are the same

>> No.6243442

>>6212418
Don't you faggots have anything more interesting to argue about? Something relevant to the world-at-large, maybe?

>> No.6243469

>>6243437
>Clearly this is not the case
Do you have a single shred of evidence to back this up?

>> No.6243484

>>6243469
>evidence
This isn't science.
Regardless, it's the fucking definition of 0.999...

>> No.6243501

>>6243484
>Regardless, it's the fucking definition of 0.999...
This is false.

>> No.6243527

>>6243501
let s(n) = sum k=0 to n of 0.9/(10^k) = 1-(1/10)^n+1 by summing the geometric sequence

suppose s(n)<x<1 => 1-1/10^(n+1)<x
Rearranging we get
1-x<1/10^(n+1)
1/(1-x)>10^(n+1)
log(1/(1-x))>n+1

Letting N = log(1/(1-x))-1 then for all n > N, x<s(n)<1
since x is arbitrary and s(n) is bounded above by 1, s(n) --> 1 as n approaches infinity

>> No.6243534

>>6243527
Lots of limits approach 1.

>> No.6243536

>>6243534
but s(n) as n approaches infinity approaches 0.999... dummy.

>> No.6243550

>>6219865
Thats one of the best ways ive ever heard it explained. Without using proofs, anyway.

>> No.6243556

We have that the real numbers with the Euclidean metric is a Hausdorff space. Then any two distinct points have distinct neighbourhoods. Let a = 0.999...

If a and 1 are distinct points, then there exists neighbourhoods U, V of a and 1 respectively with the intersection of U and V being the empty set.

If this is true then in particular, the point a does not belong to V. However if we write V as B(1, ε), then for all ε>0, a is contained in V. Thus a and 1 are not distinct points, i.e 0.999... = 1 as required

>> No.6243597

>>6219865
Also, the distance between 0.9 and 1.0 isn't meaningful in the long run. In base 2, 0.111...=1

>> No.6243626

let s=0.99999...
then 10s=9.99999...
and 10s-s=9.99999...-0.99999...=9
9s=9
s=1
1=0.99999...
OR
1/3=0.3333333...
3(1/3)=3(0.33333333...)=
3/3=1=0.999999999...

>> No.6243662

>>6243626
>1/3=0.3333333...
Hah!

>> No.6243677

>>6243626
Both of these proofs effectively assume the required identity. For a rigorous proof see here:
>>6243556

>> No.6244790

>>6243556
All you did was a proof by contradiction. You proved why we're not in a Hausdorff space.

>> No.6244802

>>6243677
>rigorous proof
hahaha oh wow

>> No.6246185 [DELETED] 

>>6243406
http://mathworld.wolfram.com/SeriesExpansion.html
series (1), x = <span class="math">frac 1 10[/spoiler]

>> No.6246194

>>6243406
http://mathworld.wolfram.com/SeriesExpansion.html
series (1), x=<span class="math">\frac {1}{10}[/spoiler]

>> No.6248165

>>6243677
You clearly don't know what "rigorous proof" means.

>> No.6249005

>>6223719
Multiplying finite number and infinite number.
lel

>> No.6249061

>>6249005
It's not an infinite number, it's a number with an infinite repeating decimal.
What you are actually multiplying is:

<div class="math">\frac{1}{3} = \sum_{i=1}^\infty \frac{3}{10^i}</div>

>> No.6251753

Retarded neckbeard mods still not deleting this troll spam even after 18 days? are they all high school dropouts?