Those people are retards.

>>3615181

Wrong. It APPROACHES one. It does not equal it.

>>3615204

Die.

>>3615207
The image was a way better explanation for anyone with a brain

>>3615207
How can you have a 'better' proof?

>>3615326
More elegant and intuitive.

You clearly don't actually study maths.

>>3615204

Any finite expansion approaches 1. An *infinite* expansion must equal one.

The infinite decimal expansion = sum (n= 1 to infinity) (0.9)/n

>>3615336
>intuitive
I don't think you study maths either.

>>3615204
Potential 8/10, I felt the stirrings of rage.

>>3615336
There are plenty of algebraic proofs (like the 1/3 = 0.3... and multiplying both sides by 3 proof) that are fine, but sticklers can argue with them due to some of the assumptions they make. Geometric Convergence is generally considered the only "rigorous" proof of this that's 100% mathematically correct, although you are right, it's not the most intuitive one by any means.

>>3615181
I dont understand this so I assume this is mathtroll

I keep thinking 0'9=/= 1

I keep lurking /sci/

How does this makes you feel?

Here's a question for the non-believers: what's the difference between .999.. (infinitely repeating) and 1?

>>3615371
Not that guy, but I feel kinda sad for you, whether or not you're lying right now.

(not math guy)

does stuff like geometric convergence come intuitively to anyone, or do people just accept it as a convenient formula after they see its proof?

i thought all math had a way to be intuitive, and wasn't just mashing of symbols and numbers.

>>3615379
An infinitely small quantity. 0.000...1

>>3615379
0.00...1
i.e. practically zero
learn to math

>>3615387
>infinitely small quantity

sup newton, how's your crackpot math holding up?

>>3615379
epsilon

>>3615379
If you are going to buy some fucking apples... or pears... doesnt matter but this is science goddamit, atoms fucking matter, there is a minimal difference

>>3615387
>>3615389

wrong, wrong

>>3615387
>>3615389
>>3615396
There is no such number in the reals. The difference between 0.999... and 1 is 0.

Otherwise, express the number that is between 0.999... and 1.

>>3615400

the difference is 0 sir. and the difference between any number and itself is 0!

>>3615371

Oh shit

Why that's wrong?

>>3615386
I think Convergences of any sort are really easy to intuitively visualize, after you see their graphs, at least. The mathematical proofs of them just solidify them even further.

>>3615400
>If you are going to buy some fucking apples... or pears... doesnt matter but this is science goddamit, atoms fucking matter, there is a minimal difference
You are insisting that 0.999... does not represent the limit of an infinite series, when by definition it does.

>>3615401
I actually knew it was wrong, but wanted to see /sci/ respond. I cannot convince people that 0.00...1 is rubbish. For some reason putting a one on the end of a row of zeroes which has no end does not strike them as impossible.

>>3615413
There is no necessary link between the length of curves in a series and the length of the limit curve of the series.
http://qntm.org/trollpi

>>3615426
They simply have not comprehended what "infinite" or "no end" mean.

To the people claiming 0.000...1 is an existing number, what is pi - 0.000...1?

>>3615404
>Otherwise, express the number that is between 0.999... and 1.
THIS

>>3615413
Because x =/= y in a scenario like this, even for infinitesimally small values.

>>3615438
The next number below pi

1/3 = 0.333....
2/3 = 0.666...

3/3 = 0.999... = 1

>>3615438
pi - 0.000...1, of course.

>>3615470
>>3615453
Express it as a decimal, or I will impale you

0.99999 = x
9.99999 = 10x
10x-x=9
9x=9
x=1

Learnt that in year 8.

>>3615460
I'm:
>>3615426

The same people concluded, when confronted with your proof, that 1 / 3 was actually equal to 0.333...4

Homicide, appealing sometimes.

>>3615490
Express pi as a decimal. Include all digits.

1/3=.33333...
.999.../3=.33333...

If anyone asks or says otherwise just show them this and they'll understand.

I find it funny that teachers use the 0.333 * 3 argument to prove this, and the people who just a second ago said .999.. != 1 don't just claim that 0.333... doesn't equal 1/3.

>>3615494
0.99999 = x
9.99999 = 10x
10x-x=9
9x=9
x=1

math doesn't work like that... If you subtrack x from 10x you must also subract an x from 9.99999 so it would look like this:
0.99999 = x
9.99999 = 10x
10x-x=9.999999-x

>>3615697
He's correct, he just didn't write down all every single step.

9.999999-x = 9.999999-0.99999 = 9, which is what he had.

1/3=.3...
3*1/3=3*.3...=.9...
3/3=1=.9...

>>3615336
In fact, do study maths.
Elegance is subjective, and I think that the proof in that picture is much more elegant than a fractions proof by virtue of being more rigourous.
Thinking of proofs like pictures, other proofs from the wiki page are rather blurry. This geometric series proof is crisp, vivid, in focus.
There is no objective way to say one proof is better than another - it's either valid or it isn't.
This makes me think it is you that is not actually studying mathematics at a meaningful level.

It is true. People don't understand the concept of infinity.

Take any calculator. Type a decimal point then 3 until there is no more room on the screen. Then multiply it by 3.

The answer is 1.

Ask them what they think .999.... / 3 is. If the say anything other tan .333... punch them in the dick. Ask them to express it as a fraction. If they don't say 1/3 stab them in the dick. Now ask them to multiply that by three and ask what they get, in decimal form.

>>3615779
Some of us have.

But no one who argues 0.999... =/= 1 knows a single fucking thing about it, and it does nothing to justify the faggots who troll about it.

> you can't travel at the speed of light
> only a fraction of it, 0.999...
> 0.999... = 1
> you can travel at the speed of light

Pick any 1 or 2 digit number and divide by 99, e.g. 5/99 = 0.050505... or 12/99 = 0.121212... or even 37/99 = 0.373737... etc. so have a guess what happens when you divide 99 by 99? 0.999999... right? Right?

>>3616133
its only a fraction of 1 if it terminates.

>>3616201
> 1/1 isn't a fraction

>>3615163
incontrovertible proof.

>>3615163
You do realize that nobody that matters really cares about this, right?

>>3616295
>I don't understand how this can be, so I will protect my ego by devaluing it.

>implying .999~ = 1

the limit is 1, it is not equal to 1

deal with it

oh is there a rounding rule I didn't know about

>>3616471
-3/10

>>3616499

>An infinite number of 9's followed by a 6

LOL

>>3616499
This


/thread

you are all losers who don't understand basic arithmetic

>>3616499
You should feel bad for even trying, none of that makes sense. In no way are the infinite 9's produced by our counting system analogous to points on a line. If you DID want to make the illustration, you could just as easily say that the line segment consists of infinite points (the 9's) but is still a finite span (1).

If 0.00...1 exists and is a number, then it has a place on the number line.

Suppose, like some claim, that 0.00...1 is the number directly after 0, such that no numbers exist between 0 and 0.00...1; (0.00...1)/2 should also exist. However, if so, it would exist between 0 and 0.00...1.

Therefore, 0.00...1 can not exist as defined by the crowd who believes that the difference between 9.99... and 1 is 0.00...1. If it did, it would create unresolvable contradictions.

>>3616537
If you are honestly not a troll I feel sad because of you.. what are you here?

You can't add a 6 to your fucking jew line... because whatever place in the line your 6 is at... has to be a 9 and therefore can't be a 6. You could turn that 6 into a 9... what does that shoe other than you hadn't an infinite number of 9's to begin with.

>>3615181 Is proof. Not some herpdaderp proof either. actual proof. Why are you arguing with it?

>>3616499
can't tell if troll or stupid

>>3616591

>Suppose, like some claim, that 0.00...1 is the number directly after 0, such that no numbers exist between 0 and 0.00...1

only people who say that .999...!=1 would claim something as absurd as that.

>>3616617
That's the point of proving it doesn't exist, friend. It's called a proof by contradiction.

>>3616616
see
>>3615181


I presume you were the one who thought of that line rigmaroll aswell, huh?

>>3616616

You cannot place number after an infinite number of numbers.

>>3616632

You haven't contradicted anything so far.

ask them what 1 divided by 3 is. ask them if the fraction 1/3 isn't equivalent to the decimal .333...

it's two methods of representation, they are the same number.

>>3615163
So, OP.

Let me get this straight

1/3 + 1/3 + 1/3 = 1

That is deep man.

>>3616670
The idea that if I were given the fraction 1/3 and asked to evaluate it, that I would end up with a number that is different from what I started with is insane.

>>3616677

Imagine a normal number line that extends to infinity.

Here it is.

____________________________

Now place a 5 after it.

____________________________5

I just placed a 5 AFTER the number line. Its not even on the number line ffs.

anything is possible when you use lines to do math because my brain can't handle infinity.

>>3616677
No you can't. And you haven't.

It's like me saying.. nothing can go faster than light in a vacuum . right?

c+1mph oh look I just did it.

Awesome logic /b/ro.

I just can't wait for summer to be ovver guise.

0.9 ad infinitum isn't 1
0.1 ad infinitum is what is between the 1 and the 0.9

fucking
accept it
nerds

>>3616811

-10/10

This thread is bad and you should feel bad.

>>3616811

.9 ad infinitum isn't 1 LOL

just
accept it
people with Ph.Ds in maths and physics. LOLOMGwtf!1

>>3616814
Read
>>3615181 and cut out the middle man.

You cannot add a number after an infinite set. There's no fucking room left, as infinity has filled it.


You realise that this (.999=1) has been in countless mathematics books taught in schools and colleges around the world... do you honestly think that you have "disproven"(lol funny word) a mathematical idea with your lines?

>>3616819
It's not you cunt, it's just called that way for practical purposes.
For all intensive purposes, not even the universe is unllimited, hence the ending of an "infinite" number.

>>3616811
right, because .99 + .11 is 1.

>>3616849
yes

>>3616811
You rea;ise what .1 ad infinitum is yeah?.. it's .11111.... the difference between .999 and 1 is .001. Not .111.

People are trying to say that .000000...1 is between .999 and the 1. But they think you can add something after an infinite set.

>>3616847

wow. maximum overtrolling enabled.

>>3616854
Really? because even my fucking dog would disagree with that one.

>>3616878
Your dog's cool.

>>3616888
> You cannot add a number after an infinite set. >There's no fucking room left, as infinity has filled >it.

>Hilbert's Hotel would like to have a word with you.

Nice reading bro. this has nothing to do with your jew hotel. You can have an infinity of hotel rooms yes. But you cannot have one more than infinity. Which is in essence what you did by attempting to add a number after an infinite number of numbers.

.999...=1

Prove me wrong.

0.999..... = 1 - (1/∞)


/thread

>>3616843 You cannot add a number after an infinite set. There's no fucking room left, as infinity has filled it.
Ne.

i think by the time of /sci/'s 5th anniversary, people on /sci/ will be qualified to be US middle/high school teachers. Schools will be looking for people who have enough mental patience to deal with trolls and retards without killing themselves. Anyone who has survived /sci/'s natural selection process will be eligible, as there will no one in the US who is still alive and is willing to teach American students in dumbfuck hicksville or retard ghettoland.

>>3616975
Somebody was overmedicated today huh

>>3616931
> You can have an infinity of hotel rooms yes. But you cannot have one more than infinity.

> Does not understand Hilbert's Hotel

You can have an infinity of guests. But, you can still add more after all rooms are full.

You can't add a digit to a line of infinite digits.
Putting a 1 at the end of the line means you're assuming there's an end to put it there. But it's an infinite line of digits- there isn't one available, because the digits just keep going on and on.

Here's my seeing it. 0.99999 and 1 are infinitely close, but I think the real problem lies with the numeric system.

Take 1/3 for example. If you write it out on paper and pencil, you'll get 0.333333333, with a remainder of 1 each recursion. But no matter how many 3s you write, the equasion will never be complete. So you assume, that multiplying 0.333333333... by 3, you'll get .99999999. In contrast, you've divided a number by three and multiplied it by 3 again, so you're back to your origin- that is 1. So by coherent logic, 0.9999.. is equal to 1. However, this isn't completely true. That 0.333333... you've written down was never complete. It can never be. It is because of that remainder 1 that you've never written down, that prevents this (seemingly) endless line of 9s from being the actual 1.

It's more accurate writing numbers like that in fraction.

>>3617001

>after all rooms are full
There's your problem. No matter how many guests come in, the rooms will never, ever be full.

>>3617009 You can't add a digit to a line of infinite digits.

limnnk=110−k+a10−(n+1) 

>>3617020 No matter how many guests come in, the rooms will never, ever be full.
A bus with (N) guests arrives

>>3617020
Yes, they are.
Each natural number has a room attached to it: 1, 2, 3, 4, 5, 6, 7, 8, ... N, N + 1, N + 2, ...

And every single room is occupied. ALL OF THEM.
You can STILL add another guest, though, because that infinitude of numbers is finite in comparison to higher level ordinals.

>>3617009 You can't add a digit to a line of infinite digits.

...151413121110987654321 represents my digits.
I'm going to add a 0 after them.
...1514131211109876543210

In the opposite direction,
12345678910111213...
12345678910111213...0
Done.

>>3617027

An absolute value of- p(n) function. You're not saying anything.

>>3617021

>n→∞

>As n approaches infinity

Nice try.

All this bullshit with infinite sets has absolutely no bearing on the actual problem. You have yet to show how any of what you're talking about actually disproves the basic proofs given in this thread.

>If directions indicate to round
Yes
>If instructions do not indicate to round
No


Did you faggots learn nothing in school?

>>3617064 >You're not saying anything.
> Posts the words "Nice try" as a response.
> Calls others trolls.

>>3617064 An absolute value of- p(n) function. You're not saying anything.
Yeah, because that's not wide-spread notation for the cardinality of the power set of the natural numbers.

ITT Real analysis vs Non-Standard analysis.

That is all this ever boils down to.

>>3617041

>I don't understand the concept of infinity

By definition, it's impossible for all of the rooms to be occupied.

>...151413121110987654321 represents my digits.
...151413121110987654321 is an impossible number.

>In the opposite direction, 12345678910111213...0

It doesn't work that way. You're implying there's a last number, somewhere, and you could just put a zero at the end. If that's the case, that "..." has no meaning. What it really means, is that the numbers go on forever, and there's no room for that zero to be placed. Because wherever you THINK you could put that zero, there are numbers already there, and you have to keep going further down the line. There's no "end". Don't you get it?

>>3617102 By definition, it's impossible for all of the rooms to be occupied.

Occupied? :N−OccupiedUnoccupied

n−Occupied?(n)=Occupied

What's 1/3 in decimal form?

N−> (Occupied, Unoccupied)

>implying there's an a an unoccupied number in a set of infinite digits

Work on your logic.

>>3617124
That was a set. Curly braces etc.

>>3617114

It's impossible to write it all out.

guys, euler proved this in 1770. why is it still being debated

DIVIDE 1 BY 3 AND TELL ME IF YOU GET A NUMBER THAT ISN'T .333...

THEN TELL ME THAT YOU CAN'T GET 1 AGAIN BY MULTIPLYING BY 3

INFINITE SETS HAVE FUCKING NOTHING TO DO WITH THIS.

>>3617131

That makes no sense. How is there a set if the numbers keep going?
By saying "infinite set of numbers", you're effectively eliminating all of those sets. It's not infinity if you don't.

>>3617102

Whoa, wait a minute, it's acceptable for the ellipsis to follow an infinite number on the right hand side, but it's not acceptable for the ellipsis to precede the infinite number from the left hand side?

Yet you have the tenacity to claim I don't know how to conceptualize infinity. Heh.

> You're implying there's a last number, somewhere, and you could just put a zero at the end.

No, I'm not. I'm putting that zero after the infinite number. The infinite number doesn't have an end, but that infinite is still bound to a finite space. Tack the zero on after that.

> If that's the case, that "..." has no meaning.
Oh, no, ... is still important. It signifies the continuance of the infinite part.

> What it really means, is that the numbers go on forever, and there's no room for that zero to be placed.
There's no room inside the infinite number, no, but after the infinite number you can put numbers.

> Because wherever you THINK you could put that zero, there are numbers already there, and you have to keep going further down the line. There's no "end".
Don't put the number in the line. Put it after the line.

>>3617140
LINE DOESN'T END, IT'S INFINITE.

>>3617138
Occupied? maps a room number to its occupation status, and the rule for doing so is mapping it to "Occupied.". Thus, every room is occupied.

>>3617140
Right. After the number. Meaning that it's not in the number. Therefore .999999... = 1

>>3617143
_________

This line does, and it contains every real number X such that 0X1. It has two end points.

>I'm putting that zero after the infinite number. The infinite number doesn't have an end

>putting that zero after the infinite number
>The infinite number doesn't have an end
>putting that zero after
>doesn't have an end

Where's the "after" which you speak of, if there's no "end"? Your logic is inconsistent.

>but it's not acceptable for the ellipsis to precede the infinite number from the left hand side?

Yes. Because there's no "end" in the left hand side to go to. Else it is a finite number.

>but that infinite is still bound to a finite space
This is impossible. You can REPRESENT infinitiy within a finite space, but infinity itself would take infinite space to properly write out.

>>3617153
Naw, because I can still find numbers between 0.999... and 1 by putting additional numbers after the infinite part of 0.999... That's the tricky part to grasp.

>>3617166
> This is impossible. You can REPRESENT infinitiy within a finite space, but infinity itself would take infinite space to properly write out.

You're thinking too hard about making these concepts work on paper. Math is a theoretical construct. Applied mathematics uses approximation. There's a lot of things you "can't do" in real life concerning math. You can't create perfect circles, or perfect squares, or points. You create representations of them.

>>3617168
Find a number that goes there, then. Give me a distinct number.

>>3617140

>Don't put the number in the line. Put it after the line.

There is no room. In order for you to put it after the line, there must be a place to put it there. But the line just keeps going. Where's the end? There is none. So there's no room.

you can split an atom in half but you can't divide it in three.

> /thread

>>3617180
I suppose you think there's a finite amount of points in a line, in a box, in your house, in your car, in your face, in your dog. Nope. All infinities of points, and you can still place points adjacent to those infinities.

If anyone actually doesn't understand why these are equal and wants a proof starting from the basics so that its easily understandable (meaning it will be large, starting with the construction of the decimal representation of real numbers, and going on to prove non-uniqueness of representation, show exactly when this happens etc) I can write one up and scan it, shouldn't take me very long. Not going to bother if no one actually wants to see it though.

>>3617178
> Find me a number that goes there. Give me a distinct number.

09990999109992099930999N1

>>3617189
No, you can IDENTIFY more points, but you can't add more.

>>3617173

>You can't create perfect circles, or perfect squares, or points.

I fail to see why this is impossible.

>>3617206
Those numbers are not in that space. Wherever that 3 would go, a 9 would go instead.

>>3617158
THAT LINE IS NOT INFINITE, IT IS IN FACT FINITE.

A LINE EXPRESSING THE INFINITE AMOUNT OF POINTS BETWEEN 0 AND 1 DOES NOT LOOK LIKE THAT. SUCH A LINE WOULD NOT END.

IT IS ON SUCH A LINE THAT YOU WOULD HAVE TO "ADD A POINT AFTER IT" IN ORDER FOR WHAT YOU ARE SAYING TO MAKE SENSE. THERE IS NO END TO SUCH A LINE, SO WHAT YOU ARE SAYING DOES NOT MAKE SENSE.

THANK YOU

>>3617204
I can even do it in an arbitrary base if you like, so that you can see that .333... = 1 in base 4 and such, though this might make it a little less understandable for the newbies.

>>3617213
Points are infinitely small. The line boundaries of squares and circles are infinitely thin.

>>3617219
The 3 extends the infinitude of 9's.

>>3617223
This guy can't into real numbers.

>>3617223
Each number that finite line contains has a unique spot. There are infinite numbers on that line, each with its own unique place. The line does not have to extend forever.

1/3 in decimal = .333....3

Multiplied by 3 = .99999999...9

(1/3)*3 = 1.

QED.

>>3617213

i think he means that things in nature never actually add up to perfect measurements. no tree is exactly 52.5 feet high (it's more likely an irrational number), although it is only necessary to achieve a certain degree of exactness in all practical situations.

constructing a square perimeter fence of precise dimensions 25x25ft practically impossible. you're more likely to have something 25.24435...ft. x24.99845... ft.

also look up xeno's paradox if you're having trouble grasping how an infinite number of points can and does exist in any finite line.

>>3617230
>extends the infinitude
That doesn't actually mean anything.

>>3617243
No.

>>3617229
Last call for actually teaching what's going on instead of arguing in a non-mathematical manner about it....

>>3617206
Have yet to see a good definition of the number 0.999...N

I mean, I can "affix" a new number to a given number in any fashion I want.

N
0.999... is the number you get when you affix another natural number above the leading 0. But what value does this represent? Who knows? I just made it up.

Same deal with 0.999...N

>>3617245

The original foot long ruler was exactly 1 foot long, because when people wanted a measuring system they chose something and decided, "Hey, that's exactly a foot long!" and went on from there.

Therefore, there is such a thing as exactly a foot long: the original foot long ruler.

>>3617266 Have yet to see a good definition of the number 0.999...N
There you go: >>3617021 (a = 0..9)

>>3617266

>>3617279

Alright, I'll play your game. And I'll prove it wrong using your own logic.

Suppose you had 0.99999...N. What preceeds the N? What exceeds it? As in, what are the digits before and after N?

YOUR ASSUMPTION IS THAT BECAUSE A FINITE LINE WHICH HAS AN INFINITE AMOUNT OF POINTS HAS AN END, THAT INFINITY HAS AN END AND THUS A PLACE "AFTER" IT. YOU ARE WRONG.

>>3617279
Demonstrate to me that this number >>3617021 is different from 0.999...

>>3617292
Before a, there are n nines. At the a (which is at position n+1) there's a. If you do the limit the a term is zero of course, but that's not what was asked. It's a well-defined way of writing 0.999...N, which turns out to be a silly way of writing 1.

>>3617266
The Nth ordinal infinitude listing after 0.999...

09991=09991
09993=09993

It applies to all reals.

=31415
1=314151

>>3617298 Demonstrate to me that this number >>3617021 is different from 0.999...
It isn't. Both summands converge, the first one to 1, the second one to 0, sum is 1.

0,3333333333.... = 1/3
0,6666666666.... = 2/3
0,9999999999.... = ?

>>3617305
>>3617309

Neither of you are answering the question.

What number comes before and after N?

I want a digit. 0? 5? 3?

Give me the numbers before and after N.

From there on, I'll ask questions which you must answer in either a yes or a no. And strictly ONLY a yes or a no.

>>3617305
You're being ridiculously pedantic here. The 0.999...N that you propose is not equivalent to what >>3617206 is suggesting.

Yes, of course you can define a FINITE decimal of all 9's and ending with a digit N. >>3617206 is proposing that after an infinite sequence of 9's there comes an additional digit that is affixed to the "end".

If you've nothing to add, just get out.

>>3617326
Before: 9.
After: The number ends with N. There are no numbers behind it.

>>3617326
Nothing comes before or after the N. In the ordinal below it, you have an infinitude of 9s, in the ordinal above it, undefined.

>>3617333
Josef is trolling. We're distinct posts. Disregard him for he has no knowledge of internal set theory or ordinal analysis.

>>3617337

>Before: 9.
>After: The number ends with N. There are no numbers behind it.

But you just said Before N: 9.
And then that there's nothing behind N.
Explain. Did you mean "After: none" ?

>>3617350
It would be trolling if I had said something incorrect. Since my statements so far were true you may call me a dick if you like. Also I enjoy discussing this topic with mathematically illiterate people. It won't become any clearer than >>3617021.

>>3617360
I clearly see you now for the troll you are and will disregard your statements now and in the future.

>>3617367
Hey, what did I write that "dick" sentence for?
(Also: you don't know me, so you're a newfag. You post in 0.999... threads with a serious attitude, so you're an uneducated newfag. Nothing of value was lost.)

>>3617355

Answer the question Joseph.

>>3617376
I meant to say

0999N:=limnnk=110−k+N10−(n+1) 

brb, brushing my teeth.

>>3617384
Patently false.

>>3617379

You're avoiding the question again.

Answer this with a yes or a no.

0.9999999...N

You are saying, that the N preceeds with a 9, and there is no digit after N. Is this correct, or incorrect?

Answer with only "correct" or "incorrect".

>>3617384

see
>>3617393

Same thing

>>3617396
That's a first semester math equation. You didn't really expect him to understand that, eh?

>>3617393
Incorrect. N is preceded and followed by no other numbers. In the ordinal below N you have 0.999..., in the ordinal above N, you have an undefined quantity.

>>3617400
>>3617396
I had already answered, many posts above:
>>3617341

>>3617384
http://www.wolframalpha.com/input/?i=limit+as+n+goes+to+infinity+of+%28sum%28k%3D1%2Cn%29%28%2810^-k
%29%2BN*10^-%28n%2B1%29%29

>>3617384
Oh, there's a factor 9 missing. Anyway, good night, it was fun.

Pic's not so fun but related to OP.

>>3617400

You are still avoiding the question.
Until you answer it with "true" or "false", I will label you a troll.

>>3617401

So what you are saying is "There are no digits before and after N
Therefore, N is not part of the number "0.99999..."
Otherwise there would be ....XXXXXNXXXXXX (labeled X because you did not answer, so it is unknown)

>>3617413
N extends the infinitude of 9's. The 9's repeat forever, but the N lies outside that bound. The 9's lie inside the bound that N lies outside of.

>>3617419
So what you're really doing is just making up a number that goes between 0.999... and 1, and saying that because there's a number there, the two are not equal.

Rather like the theists, isn't it... deciding first that the proposition is true or not and then desperately seeking evidence to support it, even to the point of having to make something up.

>>3617419

So, in other words, N is not part of the number. You've just admitted there's no place for digit N in the endless 9s.

>>3617419

>N extends the infinitude of 9's

It's impossible to exceed infinity. The N does not exist

>>3617419

>The 9's repeat forever, but the N lies outside that bound

How? The 9s go on forever. There is no "beyond forever".

Think about time. "After forever, I'm going to play ball!" There is no "after". Forever just keeps going, well- forever! No matter how far you go into time, you'll -never- reach forever. You'll only be moving toward it.

I'll put it into more simple terms. Your putting N after endless 9s is like digging dirt from under a bottomless well. How will you get it? It's bottomless!

>>3617419

>but the N lies outside that bound

there is no bound. The 9s go on forever, remember?
That's why there's no place for "N"

>>3617434
it's really funny because 1 = .999.. can be proved in trivial fashion. I don't who told him that 1 = .999.. can be disproven using infinite set theory (probably no one because that's wrong). I can find no other example of this revolutionary information.

HEY

FUCK MATH

>>3617440
> So, in other words, N is not part of the number. You've just admitted there's no place for digit N in the endless 9s.
N is part of the number 0.999...N.
The 9's are infinitely recurring. N appears after those 9's.

>>3617449
>It's impossible to exceed infinity. The N does not exist
Welcome to the thread. See ordinals. It is possible ot exceed infinity. An infinite amount of things lies in every finite space. The 9's in 0.999... are endless, but still finite. N occurs after that.

>>3617473
> Think about time. "After forever, I'm going to play ball!" There is no "after". Forever just keeps going, well- forever! No matter how far you go into time, you'll -never- reach forever. You'll only be moving toward it.
We're talking math here, not making silly analogies that are nonsensical.

>>3617492
> there is no bound. The 9s go on forever, remember?
Infinity is still held to a bound.

Don't take my word for it, guys. Do your own learning.
http://www.math.princeton.edu/~nelson/books/1.pdf

>>3615163
>this thread
>still getting 100+ replies

just delete this board please.

0.99...=1
it's a flaw of mathematics, any good mathematician will tell you that, just ask your teachers

>>3618690
No, it isn't... No 'good mathematician' has ever suggested the decimal system would provide a unique representation for numbers, nor was it designed to do so, and nor is it any issue whatsoever that it does not.

ah

>>3618678
>N is part of the number 0.999...N.
>The 9's are infinitely recurring. N appears after those 9's.

Would it help this little argument along at all if I were to point out that 0.999...N is not a decimal representation? Or that if you're going to take it to be similar to a decimal representation (in that the N is the (n+1)th term of a series in a limit as n goes to infinity) that this is exactly equal to .999... and to 1? I assume this number was being used as an attempt to fit something between .999... and 1? It is equal to each of them, so it doesn't fit in-between.

Haven't really been following but I thought I might point these couple of things out, if they haven't been already. I mentioned earlier that I'd be happy to show anyone who doesn't properly understand decimal representation its construction, as well as a proof that any terminating decimal has two decimal representations... Too late now though, I'm going to bed.

>>3618687
I hate this shit too, but if you want the board gone you can just stop browsing it and then it's as good as gone, as far as you're concerned.

Sage for no bumping.

>>3619007
I'm afraid to tell you that sage does not work, and that I would not have seen this thread had it not been for your post. Your sage served only to bump the thread twice.

>>3618997
> Would it help this little argument along at all if I were to point out that 0.999...N is not a decimal representation?
Not really considering 0.999...N is a decimal representation.

>>3619184
I can look at 0.999... and tell you the position of each 9.
For example, there is a 9 in the tenths' place.
There is a 9 in the hundredths' place.
There is a 9 in the ten-millions' place.

Where is this N you speak of? What is the position?

>>3619184
at which decimal place does the N occur?

>>3619193
> Where is this N you speak of? What is the position?
>>3619191
> at which decimal place does the N occur?

The first "ones" place after the infinitude of 9's.

>>3619184
Lolno. Not in the real numbers.

I think you can do it in p-adic numbers though, but that's largely because the notation has a different meaning in that case.
http://en.wikipedia.org/wiki/0.999...#p-adic_numbers

>>3619198
>after the infinitude
No.

>>3619198
> The first "ones" place after the infinitude of 9's.

so, what's the number of the decimal place? if it's at some point in the decimal expansion, just tell me which point. the 10th? the 100th? which one?

failure to answer means it's at no place.

>>3619208
>>3619204
Yep. The ordinal of natural infinity is constructed by counting 1, 2, 3, 4, ... for each natural number. The next ordinal is that of the real numbers. You can place numbers in the degree of that ordinal adjacent to a number represented in the ordinal of natural infinity.

I don't understand why do these threads still get more than 100 replies.

>>3619212
Think of it this way.
_____________
This line has an infinite number of points on it. Each point represents a place-holder for one of the 9's in 0.999...
_____________N
That's where N is. In the first ones' place after the 9's.

>>3619223
I hope you're trolling, because your post is both very wrong and yet requires at least a limited understanding of uncountably infinite sets to be even made.

And that's really where the problem is. This set of digits is countably infinite, not uncountably infinite. If there is a "last" 9, it's not a infinite series of 9's.

>>3619216
A perfect storm of teenagers, trolls, and a few people who know their stuff and are bored.

>>3619230
Stop misdirecting your attention to this idea that I'm suggesting there's a "last 9". I know there is no last 9. I understand what infinite means. The 9's never stop repeating. I get that.

There's a little machine that sits there on the side of the road and continually spits out 9's all day long.
Next to that machine, is an N.

I can't explain it any clearer.

how the hell is sci so easy to troll?

by that i mean: how is this topic even worth discussing?

this is the type of maths questions people who failed maths argue about, not actual intelligent people

could we at least up the trolling to "cardinality of reals = cardinality of integers" trolls?

>>3619223
yep, you failed to specify the number of the decimal place that N occurs. thus, it occurs nowhere. bye bye.

>>3619230
>implying there is such thing is uncountability

>>3619249
count the real numbers

>>3619246
It occurs at 1, after the 9's, to be technical.

>>3619184
I'm sorry, but you're wrong, any digit in a decimal representation must have a finite place value, your N does not, therefore your representation is not decimal.

>>3619251
No. You are as much of a faggot as the rest of the scifags in this thread.

For example, labelling the first proof as 'proof by induction' when you clearly have zero idea what that means.

Don't argue. You know you're not educated in this area. You are wrong and you look like an idiot.

>>3619241
many people on /sci/ are total dumbasses looking to increase their intelligence but they fall into pitfalls like this thread all the time. because grasping a concept that isn't intuitive is, for many, the hardest level of intelligence to attain.

>>3619260
that is not a number. keep trying.

>>3619262
Where is there such a number that doesn't have a finite place value?

>>3619251
Please delete that now, your proof relies on the assumption of its own truth, and claims to be an induction proof while making not even the vaguest reference to induction... Or being a proof.

>>3619268
Yep, it is.

>>3619239
You have not answered my criticism, which I thought was also pretty clear, on the nature of countably or uncountably infinite sets. Perhaps you don't know the difference.

You're twisting your analogies to fit your conclusion. The "last" digit must occur in the same way that the other digits occur. But if you make your analogies consistent in this way, you see the argument fall apart.

>There's a little machine that sits there on the side of the road and continually spits out 9's all day long.
>Next to that machine, is an N.
No.
There's a little machine that sits there on the side of the road and continually spits out 9's all day long, forever.
After it has spit out 9's forever, it spits out an N.

See the problem?

>>3619264
>posts complaint
>fails to make sense

Firstly, I ripped the titles from a different version. Secondly, http://en.wikipedia.org/wiki/Mathematical_induction

>count the real numbers

1, -2, 3278, sqrt2, 2.3, pi, pi^2+e^0.999999, googleplex, etc

>>3619264

that poster didn't make that image, but elaborate how it's not proof by induction. do YOU know what it means? because nigga you just went full retard and make a goddamn fool of yourself.

>>3619249
>denying uncountably infinite sets
I'm not surprised, considering the entire topic is the real numbers, which comprise an uncountably infinite set.

>>3619277
That works, too. If the machine spits out a decimal point before the infinite 9's, and an N, after the infinite 9's, you have a number between 0.999... and 1, which shows they are not equal.

>>3619270
The N, I just said that...

0.999...N
0.999..|->N<-|
N does not have finite place value, the representation is not decimal. I mean I like the argument about affixing an N after the infinite 9s, but tell me that that is decimal representation and I will continue to tell you that you are wrong until I am blue in the face.

>>3619273
The first two do, but they use conventional knowledge to show it's true. Look at the third for a different proof.

>0.999=1 thread
>correct answer with proof in first reply
>still 203 posts and 10 image replies omitted. Click Reply to view.

the reals are countable

all proofs as to the uncountability of the reals begs the question or assumes the existence of contradictory numbers.

>>3619288
It has a finite place value of 1. It's the second 1.

>>3619279
Holy shit. You are actually arguing about this.

You are a fucking failure at life. I have zero idea how anybody could be so arrogant and stupid as to argue they're right when they KNOW they have zero education in this area. How many friends do you have?

Okay then you dipshit: if that was a proof by induction, please describe to me what the general proposition is, where you proved the proposition in the base case, and where you proved that the proposition for n implies the proposition for n+1.

>>3619241
>could we at least up the trolling to "cardinality of reals = cardinality of integers" trolls?
But then you can't argue by bullshit intuition anymore, and the trolling falls apart.

Anyway, I love the proof that the set of all point in R can be mapped one-to-one to the set of all points in R^2, showing they have the same cardinality. Fun times.

Also Hilbert's Grand Hotel, for countably infinite sets.

http://en.wikipedia.org/wiki/Hyperreal_number

OP, specify your field or face the consequences

>>3619300
>the reals are countable
>all proofs as to the uncountability of the reals begs the question or assumes the existence of contradictory numbers.
Nice try, but no.

Between any two different real numbers, there is an uncountably infinite set of real numbers. You can map the entire set of integers one-to-one to the real numbers between 0 and 1. Or between 0 and 0.1 Or between 0 and 0.01.

>>3619303
Is a set of non-intersecting loops in the plane countable?
What about a set of non-intersecting two-petalled roses (two loops joined at a point).
Good luck bro.

>>3619301
Okay then, fair enough.

No two digits in a decimal representation share a place value, here two do. Therefore the representation is not decimal.

>>3619319
They don't share the same spot, though.

>>3619303
that sounds like it would be a pretty trivial proof

god i hate maths. university was such a disappointment

>>3619316
I believe you mean can't.

>>3617309
this
l2ordinalanalysis tards

>>3619323
They don't have to, you said their place value was the same.... More importantly if you try to assign N any finite place value you run into the issue that you have infinitely many 9s, each with a finite place value, so all the finite values are taken. I'm done arguing this since you're clearly just trolling.

The thing you seem to be missing with this troll is that a non-terminating decimal representation is NOT a real number. The equal sign is incorrect, you would need to use the squigly one that means it's similar to, or an estimate.

1/3 times 3 equals one.
1/3 as a decimal is approximately .3 ad infinitum
.3 ad infinitum times 3 is .9 ad infinitum
.9 ad infinitum is approximately one.
.9 ad infinitum does NOT equal one.

>>3619351
noep

>>3619337
>you said their place value was the same....
Nope. Never said that.

>More importantly if you try to assign N any finite place value you run into the issue that you have infinitely many 9s.
We are already discussed this. The N occurs after the 9's. You agreed to it.
> I'm done arguing this since you're clearly just trolling.
Suit yourself. Trolling would be presenting information I knew was false. I know otherwise.

words cannot describe this thread.

>>3619351
>a non-terminating decimal representation is NOT a real number.
>implying pi is not a number
>implying sqrt(2) is not a number

You just denied that irrational numbers are numbers.

>>3619351
they are equivalent even if they are not equal. you can replace 1 with 0.999... in any equation without changing a thing (working with the reals of course).

nice to see the 'proof by induction' faggot and his samefaggot friend shut the fuck up, anyway.

1-0.9...=0.0...

0.infinite 0s and then a 1, but the one is never put!!!! becoz ofinf 0s
everyone understand now??

>>3619369
>they are equivalent even if they are not equal.
This is inconsistent, a blatant contradiction.

They're equal, and the difference between them is 0.

>>3619383
Wait, you can't put a 1 after an infinite amount 0's, but it's okay to use conventions like 31=0333. In the same respect, you can't write all those 3's either. This isn't about making math physically adaptable. It's the concept of math that people fail to understand.

>>3619392
so you admit there's a difference.

>>3619392
The difference between them is greater than 0.

>>3619364
Okay, maybe you didn't say it, but someone said
> It has a finite place value of 1. It's the second 1.
Anyway, my point stands regardless. In any decimal representation each digit corresponds to exactly one place value, and each place value to exactly one digit, each place value is also finite. The N in 0.999...N clearly either does not have finite place value, or shares a finite place value with another number, or does not have a place value, so what we have is not a decimal representation.

>>3619367

I am not claiming that irrational numbers and Pi are not real numbers, but read carefully here. IF THE DECIMAL FORM DOES NOT TERMINATE IT IS NOT THE EXACT NUMBER.

Pi does not have an exact decimal form, therefor any number produced using Pi is not an exact value, but Pi is an exact value. It just can't be converted to any fraction or decimal form without some value loss.

>>3619410
N maintains a separate finite decimal spot after the infinite decimal spots before it.

>>3619405
in 0.333... i can always tell you what the nth digit is.
with 0.999...N you can't tell me which digit the N is at.
> mfw when you think they both have the same problem

>>3619420
I already have many times in this thread. Stop repeating the same arguments over and over. 1

>>3619419
A separate finite decimal spot you say? Okay, let's call its finite place value n, but what's that? Oh we already have a 9 with place value n. Shame. I suppose at this point I should point out that place values have to be positive integers too...

>>3619427
just ignore them dude. you already showed 0.999... and 1 are separate numbers, now they're just picking apart trivial things they dont grasp

This thread made me think of this.

>>3619430
> The place holders have to be positive integers.

Label all the place holders in this number for me please:

168.35

>>3619427
You're not aware that ordinal numbers don't have decimal representations then? I believe you misunderstand the concept of a decimal representation rather profoundly.

>>3619405
>infinity
>after
CAN'T DO THAT

>>3619439
168.35
| First decimal Place
168.35
| Second decimal place.

Was there a point to this exercise?

>>3619440
I'm not using the ordinal itself. It's a real number inside separate ordinal spaces, because the first ordinal after the natural infinitude includes the reals.

>>3619447
That didn't work out quite how I intended it to. The three is the first, the five the second.

>>3619447
You can't use different labels on the same spot. You've failed to provide anything worthwhile to this thread, but you have tenacity to call me a troll.

>>3619450
Either way you've excluded the possibility of it being a decimal representation....

>>3619451
And the 1, 6, and 8? Let me pretend to be you...

YOU CANT PUT THOSE THERE BECAUSE ALL THE POSITIVE INTEGER PLACE HOLDERS ARE FILLED UP BY SOME MAGICAL POSITIVE INFINITY.

>>3619462
Here's the decimal representation:
0.999...N

>>3619466
In what way is that representation decimal? If you were to claim that what you were doing was analogous to a decimal representation, as I said in my very first post, I'd be more than happy to agree, if you can construct a proof that that is a decimal representation, I'll eat my words, but while you're just claiming it to be, and showing a misunderstanding of what constitutes a decimal representation I cannot see how you're anything but a troll.

>>3619464
Sigh. You're obviously not the learned anon I'm trying to discuss this with, because you're a moron. Decimal places come after the decimal point.

>>3619475
I suppose I shout point out that that is in reading left to right, and that by decimal point I mean the .

>>3619475
Place values and decimal places are distinct objects. You said place values. This thread is no longer about 0.999... equaling 1, it's about clowns like you arguing over silly concepts that are self-evident, AND, in the case they are not evident, learning material was provided.

> Prove its in decimal notation.
0.333...
0.142758...
0.999...N

That's how it works.

>>3619487
About place values and decimal points, you're right, they are different things, each of which adheres separately to the rules I was talking about. My mistake for saying place value when I should have been saying decimal place value, would you like to read back over my posts and imagine that the 'decimal' had been there, then come back and oh wait.... If that is how you believe a proof works, I'm done.

>>3619505
Just for clarities sake I'll go over my proof again, point out its flaw and provide one of your own if you please...

Each decimal digit has a unique finite positive integer decimal place value, and each decimal place value is uniquely associated to a decimal digit. Here N and one of the 9s either share a place value, or the N has no finite place value, therefore this representation is not decimal....

> 267 posts and 14 image replies omitted. Click Reply to view.
Jesus H motherfucking Christ. How can people be so easy to troll?

>269 posts and 14 image replies omitted. Click Reply to view.
/sci/.... come on now. This is ridiculous.

0.999... = ?
Stranger 1: a number
Stranger 2: .999
Stranger 1: :)
Stranger 2: obviously
Stranger 1: its 0.666 if u turn it around
Stranger 2: or 666666...
Stranger 2 has disconnected

>>3615346
not true btw
its infinity

>>3620714
You forgot your sage.

>>3620733
/sci/ can't into convergence

>>3619530
> N and one of the 9s either share a place value, or the N has no finite place value, therefore this representation is not decimal.

N does have a finite place value. Its finite place value is 1 after the succession of infinite 9's that occur. I understand that infinity seems unbounded to you. Natural infinity is bounded, however, with a simple line segment.
______________
All the 9's have a place on this line segment. Each point in this line segment represents a single, exclusive 9 in 0.999....
N occurs AFTER those 9's. N still maintains a finite value because the line is finite in length.
_______________N
The number of "place values" or "decimal points" in a decimal expansion can be viewed as the cardinality of the real numbers.
>>3619505 > My mistake for saying place value when I should have been saying decimal place value.
You are forgiven. A real infinitude ordinal extends natural infinity. Routine high school mathematics will treat the number of decimal places after the decimal point as a natural infinity. Internal Set Theory will treat that number as a real infinity. This allows additional values to occupy ordinal-valued decimal places. This in turn produces numbers between 0.999... and 1.

>>3620744
sum (n=1 to infinity) (1/n) ?
it's the harmonic series (ask wiki)

>>3620762
Please go away.

FGS

I can't post the revised version of the image. imguring it.

>>3620757
you sir are either
a) the most powerful troll i have ever witnessed
or
b) someone who has knowledge not many people possess

i just have a hard time justifying either position

>>3620771