/sci/ - Science & Math

lets just end this right here

>People still think that 1 + 1/2 + 1/4 + 1/8... = 2

>People still think the square root of two is a number
>mfw

>>3515555
Hilarious. Oh man!! You really got us!

Successful troll is sucessful! Woohoo!!!

Is that what you wanted? Good. Now fucking leave.

Don't you have some summer reading to do before the first day of school next week??

>>3515564
>>3515567
>>3515569
>>3515570
Saging does not negate the fact you couldn't resist responding to an obvious troll. Myself included. Just saying. Don't use sage. Don't NOT use sage. Don't reply. Period.

Here's what finally got me to understand it

If you assume .999... does not equal 1 then there is a difference between the two. Which means you can subtract one from the other to have a number that isn't 0. At first glance, 1 - .999... is equal to .000...1. That is an infinite amount of zeros after the decimal, followed by a 1. This number, however, does not exist. You can't have an infinite amount of zeros and stop somewhere and say 'I think I'll put a 1 here now', because then it is no longer infinite. An infinite of zeros is just that...an infinite amount of zeros, or zero, it can't be followed by something, that's not how infinity works. The difference between .999... and 1 is actually just zero, thus they are the same number.

>>3515564
Because you posted this, I'm going to bump the fuck out of this thread.

>>3515588
Well, in that case, if you can't put a 1 at the end of an infinite amount of zeros, then you can't even finish writing the number 0.999.... either.

>>3515588

Then .999... is not a number either, by that logic, neither is Pi.

>>3515589
Streisand effect on my /sci/ ?

>>3515597
Yes it is you fucking retard, those numbers go on forever, they aren't followed by anything. .999 is an infinite amount of 9's. Pi is the ratio of the diameter to the circumference of a circle. They are numbers but the go on forever. .999... is a number, pi is a number. .999...0 is not a number and pi...1 is not a number because you can't have something after infinity

>>3515593
>>3515597
kill yourselves because you don't understand what he was saying at all.

they aren't numbers, not because they go on forever, but because you can't have something after infinity

>>3515597
>>3515593

>>3515593
>>3515597

>irrational number != impossible number

>>3515608
Those numbers go on forever and ever. So, big deal? Because in order to understand them we have to approximate them at some point. Somewhere along the line, we have to stop writing digits in order to find the number, and even then, it's only an approximation. 0.9999..... is just a concept. It's a way of saying, let's just keep adding 9s as many as we'd like. If we stop, we'll be really close to 1. In fact, we can get as close as we want to 1, but we'll never BE 1.

>>3515564
Another friendly bump for this asshole.

>>3515632
>Because in order to understand them we have to approximate them at some point. Somewhere along the line, we have to stop writing digits in order to find the number

NOPE, have fun never taking a math course after high school.

>>3515646
Lols.

Have fun never understanding any math BELOW high school.

>>3515632
>in order to understand them we have to approximate them at some point

>>3515632

It's maths. The whole damn thing is concepts. Of course 0.9 != 1 in real life applications, but nobody is saying that. You're screaming at smoke.

>>3515658
I'm not screaming, but thanks for agreeing. In real life, 0.999... does not equal 1. In some imaginary world in the heads of idiots, it probably is.

>>3515555
Nice quads by the way.

>>3515564
Another friendly bump for faggy McFag fag.

>>3515666

You're totally right. Furthermore, what's up with idiots claiming there's as many natural numbers as the integers? There's obviously twice as many integers. Like for 1, you have both 1 AND -1 right?

Common sense: 1
Mathematics: 0

>.99999999...... converges to 1.
They are equal
>root2 does not converge to an actual number.
It is the same as an imaginary number

Quit failing abstract mathematics. Its not that hard.

>>3515658
>Of course 0.9 != 1 in real life applications
.999... is actually 1 in all applications. That's the whole fucking point of the argument. They are the same number, and if you still can't see why like this >>3515666 fucking retarded, then you are just as retarded.

>>3515658
You cant be serious.
This is bad. You should feel bad.

>>3515658
But they do, they represent the same number.
1 = 10/10 = 5 - 4 = .999...
In all applications it is the same number. Saying things like "hurr durr in real life it isn't" basically means you still don't get it at all

>>3515682

Dude, look. It's not difficult.

When two numbers are the same, every digit in every slot is equal.

1.2345 is equal to 1.2345

Why?
1 = 1
. = .
2 = 2
3 = 3
4 = 4
5 = 5

Is 0.999..... equal to 1?

0.999999999999.......
1.000000000000.......

I think not.

>>3515701
>>3515696
>>3515682

My bad guys, I'll let you take this from here. I'm apparently past my think limit for today. Pic related: it's what I won't be doing, but I imagine the other guy might.

>>3515701
We're talking about real life. Imaginary world has nothing to do with math.


DUDE, I JUST MADE UP THIS PLACE WHERE ALL ODD NUMBERS ARE DIVISIBLE BY 12. IT'S AWESOME. IT DOESN'T WORK IN THE REAL WORLD THOUGH. BUMMER!

>>3515708

just like how 1 + 1 =/= 2

because the slots in the digits aren't the same.

i feel ya bro

x = .999...
10x = 9.999...
10x - x = 9.999... - .999...
9x = 9
x = 1

>>3515727
My fucking point is that in real life they are the same. The exact same, god damn it.

>>3515720

and just to clarify, my mix up happened when I was trying to point out a finite amount of 9s would not be equal to 1. I don't know what happened, I guess I have a brain tumor

>>3515743
No, they're not. You're saying in one hand you have the number 1. In the other hand, you have a number less than 1.

It fucking starts with a zero, dude? How can it be 1.

If x < 1 and you add x to 0, your result is less than 1.

Zero + 0.9384938 < 1
Zero + 1/2 < 1
0 + x < 1 when x < 1

>>3515708
Yeah no.
>>3515732
That.


if you claim the two numbers are distinct, then by the power of the real line, give me another number between them.

In the real numbers you can always find another between two.

If the two are distinct.

Betcha cant find anything , therefore contradiction, they must be equal.

>>3515752
>In the other hand, you have a number less than 1
There's where you went wrong, .999... is not less than one, it is 1.

>>3515727

You're talking like this proof is based on some imaginary arbitrary pseudo-logic. It's not. It's the same maths that describes the area of a square, the differential of a function, and one being equal to 0.9..

>>3515752

The Reals are dense. We can prove that. What does dense mean? It means, between ANY two real numbers, there is a third. So if 0.9 recurring and 1 are separate real numbers, there MUST be some number strictly in between the two. Can you find such a number?

>>3515752
Numbers are concepts, you are letting notation dictate how you think. If you had .999... dollars you would have as much money as a dollar bill.

When will you babies learn limits

>>3515758
base 11 where a=10
0.aaaaaaaaaaaaaaaaaaa...
pwned

If they aren't the same then that means there is a number inbetween them. Show me that number, you faggots.

From an accounting/business point of view, it just comes down to materiality. 1 cent versus 0.999 of a cent doesn't fucking matter for vast majority of cases.

>>3515758
To find a distinct number between two different numbers, find their average.
<span class="math">0.999... < \frac{0.999... + 1}{2} < 1[/spoiler]
>>3515767
The number to the left of the decimal point is a 0. It can't be more than 1 greater than that number.

1.29 starts with a 1. It must be less than 2.
2.98 starts with a 2. It must be less than 3.

>>3515735
Seriously, also show us what's wrong with this proof because it looks pretty damn good to me, non-believers.

Yeah, if you want to USE the number .999..., it has to fucking equal 1.

WTF? Pi is a number.

>>3515789
This has nothing to do with limits. .999... is not approaching one because it actually is one.

>>3515788
but... [(.999... + 1) / 2] is .999...

>>3515799
Nothing. Because its correct.

>>3515788

nigga please, you can't have a 1 on the end of infinity, because infinity by definition has no end - how many times does this have to be explained?

>>3515788

1.9999.../2=0.9999...

>>3515788
>>3515788
No.

What is that in your numerator?
0.999...+1 ?
What the hell is that. Dont you mean 2

so its two over two less than one? I hope we don't have to convince you that's not true.


youre going to have to prove that that crazy fraction is more than the number on the left and less than the number on the right. what does it evaluate to? write it as a decimal so we can check the digits!

>always thought it was trolls trolling when they said they are the same number
>mfw the first chapter of my calculus textbook actually stated that .999... = 1 while explaining the concepts of what numbers are and how they should be treated and my professor showed me in depth why they are the same number after I asked him

>>3515806
1 is the limit. The same as how 1/infinity is zero.

>>3515588

This may very well be the best heuristic explanation of this concept. I will definitely use this.

>>3515789
Yes. Oh, fuck yes.
>>3515794

http://en.wikipedia.org/wiki/0.999......
Wikipedia even says they are the same number
What now, faggots?

Trolls. Trolls.

0.9999....with a 5 at the end.

If you can conceptualize 0.999... you can conceptualize 0.999...5 I'm sure.

>>3515919

...except the latter is a contraction and makes no sense

>>3515938

ContrDICTION! Dammit... too late

>>3515944

I'm going home.

>>3515919
>at the end
>of an infinitely long number
>intredesting.jpg

>>3515564
You need a better copypasta. You're skipping over the most important step.

Copypasta:

This is basic Real Analysis.

Natural Numbers are defined ala the Peano Axioms.
Integers are defined as Natural Numbers closed over additive inverses.
Rational Numbers are defined as Integers closed over multiplicative inverses.
Real Numbers are defined as Rational Numbers are closed over least upper bounds.

A decimal expansion is defined as a polynomial of digits whose Real Number value is its limit. This is the definition. Ex:
0.abcdef... (decimal)
= 0 . [a sub 1] [a sub 2] [a sub 3] ...
= lim as n -> inf of sum as i = 1 to n of [(a sub i) / 10^i]

0.999 repeating
= 0 . [9] [9] [9] ...
= lim as n -> inf of sum as i = 1 to n of [9 / 10^i]
= 1

Basic calculus. I love it.

These are the definitions of the relevant things involved. If you disagree, you're welcome to define your own math.

PS: Also, OP is troll or idiot.

>>3516142
I'm working on a new version of my copypasta right now. Here's some more:

Alternatively, it is a provable property of Real Numbers that A <= B and A != B iff there exists a real number C so that A < C and C < B. There is obviously no Real Number between 0.999... and 1, and thus 0.999... = 1.

Also, 0.999...9995, aka an infinite number of 9s, with a 5 at the end, is not a polynomial of digits. It is not a decimel expansion. It does not identify a Real Number.

0.999... is not a number but a limit.
And if you take any number in this limit, you can take another number that is between it and 1, so it's different than 1.
His limit is 1 but it never reaches it. Deal with it.

>>3516203
Take a basic course in physics. It would do you well.

1 = lim as n -> inf of sum as i = 1 to n of [9 / 10^i]

It's not "gets close to", nor "approaches". It's straight up and up equals.

>>3516203
Take a basic *calculus* course. It would do you well.

1 = lim as n -> inf of sum as i = 1 to n of [9 / 10^i]

It's not "gets close to", nor "approaches". It's straight up and up equals.

>>3516234
Well, calculus is wrong then.

Anyone that believes they are equal needs to be taken out and shot in the street for retardation.

Common fucking sense will tell you that something less than one, is not equal to one. The reason this can be shown otherwise is because our system of representing mathematics is imperfect, much in the same way i cannot logically exist or be represented, yet simultaneously must exist for certain applications.

.999... =/= 1
1/infinity =/= zero

Anyone that believes otherwise has trouble understanding the concept of infinity in the first place.

people still think that 1 = 1 OMG YOU MUST BE FUCKING RIGHT

>>3516234
This is a gradient you fool. It approaches 1 at a time scale. .99999999999999999999999999999 isnt 1 until it reaches 1. Fucking casuals

>>3516402
They are right. 1 most certainly equals 1. Numbers that are not one, like .999... dot not equal one however.

>geometric convergence proof on second post
>9001 posts and 420 images omitted. click here to view the full page

I hope no one here is in college yet

Okay guys... This debate is a little bit silly, so here's what we're going to do:

This is a number: 1
This is a number: 0.999...

They are both numbers! But... they are not the same number! One has a zero at the start. One has a decimal place with an infinite amount of nines afterwards. The other one, does not have a zero at the start and it does not have an infinite number of nines afterwards.

This is a fucking stupid debate. A three year old can tell you that they're not the same fucking number.

/thread.

>>3516472
>"proof" posted has poor understanding of calculus
>"lol see, u guyz r dum"

I thought /sci/ was supposed to be smarter than /b/

>>3516410
>>3516456
I say again:
>Take a basic *calculus* course. It would do you well.
>1 = lim as n -> inf of sum as i = 1 to n of [9 / 10^i]
>It's not "gets close to", nor "approaches". It's straight up and up equals.

>>3516502
>This is a fucking stupid debate. A three year old can tell you that they're not the same fucking number.
Too bad the three year old would be wrong. See:
>>3516142
>>3516156

>>3516592
>Guys, I don't really understand how calculus works because I dropped out of community college, but doesn't this sure sount smart?

See
>>3515555

>>3516472
seriously holy fuck just look at the first reply people

>>3516611
The first reply, while correct, glosses over the most important part of the proof, which is the point of contention.

>>3516503
>claims accurate proof is dumb
>doest provide any evidence for fallacies in the proof

never change

You know why 0.999.. = 1 is wrong ?
Because infinity doesn't exist.

>this thread again
>people getting trolled

>>3516645
So many things wrong.
>Implying that 0.999... implies "infinity is real", whatever that means.
>Implying that math has anything to do with physical evidence and physical existence.
>Denying the good explanations else-thread.

>>3516663
In all your proofs you have a sum going from n=1 to inf, you take a leap of faith there, because you'll have n=1,2,3...,99999,... but it never actually reaches infinity, but you pretend it does so it can prove your crazy stuff. It's like dividing by 0.
n will never reach "infinity", and the sum will never reach 1.

>>3516705
I never took a leap of faith. I said it's a definitional issue. I said that a decimal expansion is /defined as/ the limit. If you have a problem with this, then I suggest you invent your own math, and leave us actual mathematicians with actual college degrees who've studied this shit to the hard stuff, son.

>>3515837
but 1/infinity != 0
it's 0.00...01

>>3516729
>it's 0.00...01
There is no such real number. That is not a valid decimal expansion.

>>3516717
>College degree
>thinks .999... = 1

nope.jpg

>>3516705
At some point, however, the level of accuracy required negates the .00000000000000000001 you're missing.

>>3516738
Yep.jpg
Take some Real Analysis. Come back to me when you understand cauchy sequences and Dedekind Cuts.

>>3516750
>Proves ignorance with every post
>Says others need more education

My detector seems to be sensing something....

fueling the fire, don't mind me.

1/3 = 0.333... (By definition of one third)
3(1/3) = 3(0.333...) (multiply both sides by 3)
3/3 = 0.999... (Operation)
1 = 0.999... (Simplify)

>>3516737
1 - 0.999... = 0.00...01 = 1/infinity
infinity - 0.999...*infinity = 1
infinity - infinity = 1
0 = 1

>>3516775
Look. I'm not trolling. I can walk you through this again. Stop me when you disagree.

Natural Numbers are defined ala the Peano Axioms.
Integers are defined as Natural Numbers closed over additive inverses.
Rational Numbers are defined as Integers closed over multiplicative inverses.
Real Numbers are defined as Rational Numbers are closed over least upper bounds.

We can prove from this that Real Numbers are a dense Field.
Thus we can prove (for all Real Numbers A, B) (A < B or A = B or A > B).
1 is a Real Number.
If we "assume" that 0.999... is a Real Number, then we can do use the above (ala universial instantiation) to get
(0.999...) < 1 OR (0.999...) = 1 OR (0.999...) > 1
"(0.999...) > 1" is obviously false.
You claim that "(0.999...) = 1" is false.
Thus "(0.999...) < 1" is true.
As Real Numbers are a dense Field, there must exist a new number C so that (0.999...) < C < 1.
This is obviously false.
Thus one of the assumptions must be false - that is we can conclude either 0.999... is not a Real Number, or 0.999... = 1.

There's actually a much easier way of thinking about it.
4/7=.571428...
3/7=.428571...
Both of the decimals repeat for infinity.
Now, add the columns.
7/7=.999999....
1=.999999.... to infinity
QED Bitches

>>3516778
Hello, my name is dumbass. Allow me to demonstrate how I do not understand the concept of the base-10 system.

>>3516799
How the fuck did you even pass college algebra?

Oh wait. Yep. I have been trolled. 3/10 for making me respond.

>>3516849
Going to pick out anything in particular? You are the one trolling if you refuse to pick a particular point where I went wrong. If you want to claim that it's sufficiently vague that you cannot pick out where I went wrong, I can more formalize it if you want.

>>3516799
Yeah it would work if infinity was not retarded in the first place.
I tell you, it's the whole, "n=1 to inf" thing that's wrong. Doesn't make sense.
You can't approximate an infinite sum as a fixed number and then compare it with a fixed number.

>>3516849
>troll claims someone else is trolling... wow, haha

>>3516834
While I understand that his proof is not good (since it is not formal in the least), how does that demonstrate that he does not understand base-10? (Also, all cardinal number systems are base-10.)

>>3516868
So no, you're going to continue to troll, flippantly call my proof wrong, despite your inability or unwillingness to sit down and discuss constructively where my proof is mistaken.

>>3516877
Well the mistake is that 0.999... isn't a real number.
It's a bullshit number.

>>3516884
Acceptable, troll.

>>3516893
If 0.999... is a real number.
Then we have that there is no a and b integers such that a/b = 0.999...
So 0.999... is irrational.
And 1 isn't irrational so they're not the same number.

>>3516905
>If 0.999... is a real number.
Sure.
>Then we have that there is no a and b integers such that a/b = 0.999...
What? That makes no sense. 1/1 = 1 is a Real Number.
Moreover, 1/1 = 0.999..., and it is a Real Number.

The rest of your proof does not follow.

>>3515777
I thought that this was essentially an axiom of the real numbers? :P

e.g. The axiom "The order is Dedekind-complete; that is, every non-empty subset S of R with an upper bound in R has a least upper bound (also called supremum) in R."

>>3516922
>I thought that this was essentially an axiom of the real numbers? :P
This is provable easily.
For Real Numbers A and B, A != B
(A + B) / 2 is a Real Number distinct from A and B, and between A and B.
Thus Real Numbers are dense.

Supremum? Sounds like you're talking about how Reals are closed under least upper bounds, which is not the same thing as dense-ness. Rationals are also dense, but they are not closed under least upper bounds.

>>3515820
It IS possible to define a number system in which you can have something AFTER infinity :P

http://mathworld.wolfram.com/OrdinalNumber.html

BIAATCCHH!!

>>3516913
But if 1/1 = 0.999...
Then 1 = 0.999...
Which is obviously false.

>>3516868
Holy shit. This is so terrible that I just have to deconstruct it for funsies.

>Yeah it would work if infinity was not retarded in the first place.
A fundamental element of higher mathematics is retarded? Wut? I assume you heard from your pre-algebra teacher that infinite does not exist. Protip: it does. In fact, there are even different kinds of infinity!
>I tell you, it's the whole, "n=1 to inf" thing that's wrong. Doesn't make sense.
Summations are frequently made from 0 or 1 to infinity. Also, that's how many sequences are defined.
>You can't approximate an infinite sum as a fixed number and then compare it with a fixed number.
"Fixed number," you say. You seem to imply that the infinite sum for which 0.9... is shorthand is a non-trivial function or something. Protip: it is a number, not a process. The approximations one does are not the number itself, but approximations of the number itself.

That whole post reads like the most retarded "I don't understand it so it has to be wrong," rants I've ever seen.

>>3516934
Nope troll.

I was merely pointing out how the original dude was begging the question. By asserting that there is no integers A and B so that A / B = 0.999..., he asserted that 0.999... != 1. That's the definition of begging the question.

>>3516942
>>3516941
If 1 = 0.999... where does the 0.00...01 goes ?

I love how we have pure math / math&physics majors from university arguing with either:
a) Dumbasses from middle / high school
b) Trolls from pure math / math&physics

Also, >>3516142, do you really think OP is going to understand everything you listed there lol?

>>3516955
There are no nonzero infinitesimals in the set of real numbers.

In other words, 0.00...01 is not a number, and the difference between 1 and 0.999... is 0. But I think you know this.

http://arxiv.org/abs/0811.0164

>>3516965
> There are no nonzero infinitesimals in the set of real numbers.
What about epsilon ?

>>3516957
>I love how we have pure math / math&physics majors from university arguing with either:
No we don't. We have ~1 dedicated troll, and a couple of people who haven't taken anything resembling Real Analysis who think that they know what is going on.

>Also, >>3516142, do you really think OP is going to understand everything you listed there lol?
Nope, but that is the correct answer. There is no simpler way of doing it.

>>3516968
>What about epsilon ?
It's not a member of the set of real numbers. You may be thinking of different systems, like hyperreal numbers. Or you're just trolling, but whatever.
http://en.wikipedia.org/wiki/Hyperreal_number

>>3516973
LOL, my bad, I just realized the only posts written by somebody who knew what they were talking about were by you :P

>>3516142
>Real Numbers are defined as Rational Numbers are closed over least upper bounds.
Wait, does this imply that irrational numbers are not real numbers? Because I know that's not right.

>>3516996
Irrationals are a subset of Reals.
By definition, Irrationals = Reals set-minus Rationals.
Irrationals can be split into two camps, the transcendental and the algebraic IIRC.

>>3516996
No, what he means is real numbers are defined as an extension of rational numbers, by adding an additional axiom (any subset with an upper bound has a least upper bound).

>>3516996
I had a typo. I hope that wasn't the source of the confusion. It should read:
Real Numbers are defined as Rational Numbers closed over least upper bounds.

(.999...+1)/2=.999...

(x+y)/2=x
x=y

>>3517015
I must still not understand then, because it seems to exclude irrational numbers. I admit I don't know what the "least upper bounds" part refers to, but I don't know how it can pull irrational numbers out of rational ones.

>>3517022
See this:
>>3517013
>No, what he means is real numbers are defined as an extension of rational numbers, by adding an additional axiom (any subset with an upper bound has a least upper bound).

He got it absolutely right. Do you know what a closure is?
http://en.wikipedia.org/wiki/Closure_%28mathematics%29
In short, I said that Real Numbers are the smallest possible set which
1- contain the Rational Numbers, and
2- is closed over least upper bounds.
(At least the only such set up to isomorphisms.)

As Rationals are not closed over least upper bounds, thus we have to add numbers to Rationals to get Reals.

>>3517022
What that axiom means is:
For ANY subset of the real numbers that is bounded, then there is a SINGLE number which is the lowest possible upper bound of this subset.

For example, we can construct the square root of 2 in this fashion. Consider the set of numbers {x}, such that x^2 < 2. Then there must exist a number, which we define as sqrt(2), which is the least upper bound of this set.

>>3517029
Yes, I understand closure, but I didn't understand the operation in question. Thank you.

>>3516965
if you say
9/(10^1) + 9/(10^2) + ... + 9/(10^inf) = 0.999...
then I say
1/(10^inf) = 1/(1000...) = 0.0..001

And there's nothing you can do about it.

>>3517037
>And there's nothing you can do about it.
Yeah, mathematics says you're a faggot and the limit you're trying to express is 0.

>>3517037
Well, yes, you can. 0.999... is a valid polynomial of digits. 0.000...0001 is not a valid polynomial of digits.

DEAR GOD, PLEASE STOP HAVING HIDEOUSLY UNRIGOROUS ALGEBRAIC "PROOFS" THAT 0.999... = 1. THEY ARE NOTHING BUT HANDWAVING.

>>3517041
Indeed. I've been trying with:
>>3516142

>>3517039
If you think that 0.0...001 = 0
Then
1/(1000...) = 0
1 = 0
If you think that 0.0..001 exists
then 1/(1000..) = 0.0..001
1 = 1

Who wins ?

>>3517055
>1000...
This is also not a valid representation. It is not a number.

>Make thread
>Leave for errands
>Come back over four hours later
>Thread still on front page
>.999... =/= 1 has been irrefutably proved dozens of times in the thread
>All supposed proofs otherwise have been shown to be based on false assumptions and poor understandings of mathematics
>People still insist on arguing even when they know it's retarded
>mfw

>>3517064
Welcome to 4chan, we have a problem with trolls and the people who feed them.

>>3517055
The correct answer is that 0.00...0001 is not a valid polynomial (of digits). It is not a defined decimal expansion of a Real Number.

0.999... is a valid polynomial (of digits). It is a defined decimal expansion of a Real Number.

If you want to talk about non-Real Numbers which exist on the number line, then you first need to present your new mathematics.

>>3517064
>All supposed proofs otherwise have been shown to be based on false assumptions and poor understandings of mathematics

Read better. Mine have been good.

{.9999...,1}c|R
|R is a DLO
If .999...<1, then there exist a x such that:
.999...<x<1
by >>3517019
x DNE
Hence .999==1

depends on what 1 stands for

>>3517069
Well, I hereby define that 1/inf = 0.0...01

>>3517084
fail for using R when you could have just as easily used Q

>>3517090
You can't have 1/inf explicitly, because infinity is not a number. However, if you define the related limit properly, it is 0. (limit of 1/x as x->0)

So, 0=0.0....01 if we tack on your definition, but it doesn't change anything and it destroys the simplicity of the system, as this extra symbol is arbitrary.

>>3517084
As defined here >>3517090
1 - 0.999... = 0.0..01
And 0.0..01 / 2 = 0.0..005
So there exists n = 0.999...95 such as
0.999...<n<1
And 0.999... != 1 because they're very dense

>>3517073

Ah. So I see why this thread has so many replies. The dumbass with the retarded 'proof' using elementary-school level mathematics is still here.

Well, seeing as my faith in humanity is sufficiently demolished by the sheer amount of derp in this thread, and by people who absolutely refuse to apply basic logical theorems, I will be taking a page from the idiot tripfags in the thread and heading off to troll other boards.

>>3517069
> The correct answer is that 0.00...0001 is not a valid polynomial (of digits). It is not a defined decimal expansion of a Real Number.

> If you want to talk about non-Real Numbers which exist on the number line, then you first need to present your new mathematics.

>>present your new mathematics.
http://en.wikipedia.org/wiki/Non_standard_analysis

>>3517107
If we want to be evil, we can include a variety of infinities in our set of numbers. See ordinal numbers :)

>>3517112
Yep. As mentioned else-thread, moving beyond Real Numbers allows you to define infinitesimals.

0.000...0001 is still not a valid decimal expansion, and you would never see that in a non-standard analysis course.

>>3517107
>Nothing = Something
>Seriously arguing this point

Holy fucking shit. Really?

This is the reason the human race will be considered a joke were we to ever make contact with extraterrestrial sapient life.

>>3517112
http://en.wikipedia.org/wiki/Hyperreal_number

>>3517123
...
I have made no such argument.

>>3517122
>0.000...0001 is still not a valid decimal expansion, and you would never see that in a non-standard analysis course.

For all N there exist an X such that for all xєX 0<x<1/10^n
.000...01єX

>>3517140
The bad part is "for all N", and then assuming you can say "N=inf".

Reported.

>>3517148
It works for N=0.
It works for N, and you can take a new X and have it work for N+1.
So it works for inf.
And X as n = inf is the difference between 1 and 0.999..., such that they're not equal.

>>3517148
Actually, no. You just let it become arbitrarily large. Higher maths does this all the time. Let epsilon be greater than 0

>>3517163
defining infinitesimals

>>3517162
>>3517163

Why can not summer into basic Analysis?

the entirety of the ≠ argument:
>things that don't look the same can't mean the same thing

>>3517148
>For all N there exist an X such that for all xєX 0<x<1/10^n

>There exist an X for all nєN such that for all xєX 0<x<1/10^n

.000...01 falls within the set X which non-standard analysis says exist (and is uncountably infinite)

what you fags need to prove is that 1-.999...=.000...01

1/3 = 0.99...
3(1/3)=3(0.99...)
1=1
...

>>3517209
Ironically, this is more intelligent than the supposed .999... = 1 'proofs' posted in this thread.

>>3517209
try again
1/3 = 0.33...
3(1/3)=3(0.33...)
3/3=0.99...
1=1
...

>>3517209
You can't just 3 * 0.33...
Because there's all sort of weirdness going on when you multiply 0.00.0000003 which is supposed to also equal 0. You lost some of the multiplication by multiplying infinite loosy shit, if you see what I mean.

>>3517242
...
what? There is no "last" 3. That's why this 0.0...01 stuff is bullshit. That's not a number.

>>3517242
>>3517203

Define "0.00..1". What does ".." mean in the middle of a decimal? I know what it means at the end, ie, this is the representation of (for example), limit as n goes to infinity of sum from k=1 to n of 1/10^k. What does the ".." mean in the middle?

>>3517252
0.333... = 0.3 + 0.03 + 0.003 + 0.333...330 + 0.000...003
Problem ?

>>3517265
>0.000...330
fixed

>>3517265
>an infinite series on digits has a last digit

>>3517247
5 is not a number either then. You cannot arbitrarily discount a number simply because it is infinitely small. lrn2limits.

>>3517265
>0.000...003
I still don't know what this means.

>>3517277
>3*0.33...
>multiplying an infinite series of digits

>>3517286
1/(3*10^inf)

>>3517278
No, but you can discard a sequence of characters someone has typed as "not a number" because that sequence doesn't actually have a mathematical definition. "5" has a definition - the successor of the the successor of etc of 1. "0.000...001" is no more defined as a number than "cabbages".

>>3517288
>x=1.000,,,
>x×2=2=2.000...
problem?

>>3517310
But 1 is an integer and 0.33... a real number.
We don't know how to multiply real numbers yet.

>>3517301
Sure, fine. Now define "10^inf", because the definition everyone _else_ is using isn't defined for exponents outside of the complex plane.

I have no idea how you type math symbols on this board...

Sigma with infinity on top, k = 1 on the bottom, and the rule is .9(.1)^N

The sum of that to infinity is .999...

Now to since R<1, it converges.
Sum of a converging series is (a1)/(1-r), or the first term divided by (1 subtracted from r)

So it'd be .9/(1-.1) -> .9/.9 = 1.

Or you could do that:
s = .999...
10s =9.999...
-s = -.999...
9s = 9
s = 1

There are lots of ways, all of them ending in .999... = 1.

>>3517278
Saying an infinite series has a last digit is like saying their is a largest number.

>>3517332
Yep.

>>3517324
10^inf
= product for n=1 to inf of 10

>>3517324
Infinite iterations. Congratulations, you are a smart as the greeks were 10,000 billion years ago.

>>3517339
>10,000 billion years ago.
You're a funny guy. I kill you last.

>>3517337
That doesn't converge. In other words, by your definition, "10^inf = inf". So now define division by infinity, because the definition everyone _else_ is using requires the existence of a multiplicative inverse in the complex plane.

>>3517332
But infinity doesn't really exist.
0.999... is a mathematician's wet dream.
In reality, where truth prevails, nothing else than 1 equals 1, because there's no infinity to fuck around with us.

>>3517322
X=⅓=0.333...
3(X)=1
problem?

>>3517351
There is no "1" in reality. 1 is an abstract concept, a term rigorously axiomatically defined by mathematicians to manipulate in a rigorous axiomatic context. This is no more or less true of infinity.

>>3517345
I already defined 1/inf = 0.00..001
See >>3517090

>>3517366
And it was pointed out that this is really just 0.

>>3517366
Have fun inventing your own mathematics. Nobody is gonna care.

>>3517370
0.00..00 != 0.00..01

>>3517366
Your definition is recursive. Define "0.00..01" - you say, it's 1/10^inf. Define 1/inf. You say, it's "0.00..01". When we have yet to establish all terms, you cannot use terms we are in the process of establishing.

>>3515555
I'm just going to call this a bug in the whole 10-base number system. Because realy, if you can't math a number back and fourth the same way you done it, then its wrong.

then does 0.999...999...=1? (an inf. series of 9s after an inf. series of 9s)
how about 0.(999...)...=1? (an inf. series of an inf. series of 9s)
how far can you go?

>>3517376
>0.00..01
That's not a number, for the last time. It's an abuse of notation. As noted before, you might as well say "cabbage".

>>3517388
What? Are you referring to some kind of operation without a defined inverse? Because I agree, the real numbers should have those.

>>3517397
What does it mean to have something "after" an infinite series?

>>3517401
just trying to get
>>3517376
and co. to think more about what they are saying

<span class="math">\sum _{k=1}^\infty .9(.1)^{n-1}[/spoiler]

Learn that first

>>3517397
>then does 0.999...999...=1? (an inf. series of 9s after an inf. series of 9s)
It's definitional. The text "0.999..." is a sequence of digits, and it is /defined/ to be equal to the sum of that cauchy sequence of digits.

>how about 0.(999...)...=1? (an inf. series of an inf. series of 9s)
Same thing. They both are the same sequence of digits.

Protip: A sequence is a function with the domain of Natural Numbers.

The problem is simple

0.999 = 9 * ( sum of n=1 to inf of 1/10^n )

You fags believe there exists a n very big as 1/10^n = 0. Which is wrong.
However big you take n, there exists 1/10^n_big = 0.00..01 very little
It's never 0.
You say there is some moment where it's so big that it could as well be 0.
That's when you approximate 0.999... as 1, which it isn't.

>>3517423
Yeah, you fucked up halfway through.

If you take the LIMIT as n -> inf, then 1/10^n -> 0.

You just don't understand limits and infinity.

>>3517435
It's the limit, 1/10^n never reaches 0. It goes toward it.
0.999... never reaches 1, it goes toward it.

I just hope everyone knows that this shit isn't up for debate.
http://en.wikipedia.org/wiki/0.999......

And no, wikipedia is not the source, it is a collection of sources.

>>3517437
0.999... IS the limit of infinite digits. There is not a "very large" number of 9's there. The "..." means it goes on forever, and there is no "last" 9.

>>3517437
it's not (LIM 1/n as n→∞)≈0
it's (LIM 1/n as n→+∞)=0

>MFW everyone disagreeing is underaged

>>3517443
The limit of the suit constructing 0.999... is 1, I agree, but the number 0.999... with an infinite number of 9 isn't 1.

>>3517437
If you write any finite number of 9s, of course this is still distinct from 1.

However, .9999... is defined to be the limit as the number of 9s approaches infinity. "The limit" is defined to be the number L, if such exists, that for any real number \epsilon, there exists some finite number of 9s such that for any number N of 9s greater than that, .99999999 with N 9s is less than \epsilon away from L.

1 is such an L. Therefore, by definition, 1 is the limit as you write more 9s. Since .999... is defined to be the limit as you write more 9s, .999... is 1.

>>3517450
>limit is 1
>infinite number of 9's isn't 1
You're contradicting yourself.

Also, as a reminder.
>>3517440

>>3517450
wat

>>3517197
I think we have a winner

I came here a few months ago and posted the explanation as to why .999 = 1

Hopefully some of you faggots will learn something and stop acting like you can do math.

>>3517466
> 9.999... - 0.999... = 9
wrong
> 0.333... + 0.333.. + 0.333... = 0.999...
wrong
>infinite series
infinite doesn't exist. it's the dream of crazy mathematicians.

>>3517466
game-set-match
fatality
a winner is you
image saved
/thread

>>3517481
0/10, try to be more sincerely misunderstanding instead of crackpottish next time

>>3517481
does 1/3=0.333...?

>>3517490
yes

>>3517481
>>3517481

come back to have a conversation when you graduate grade school.

>>3517490
wait. no.
fuck

>>3517494
does 3(1/3)=1?

>>3517499
It's correct.

>>3517499
HAHAHAHAH
FAGGOT

>>3517500
Yes by definition.
But it doesn't make sense to multiply numbers with infinite precision.
That's why 3*0.333... != 0.999...
You can't just do that.

>>3517496
.99... does not equal 1 otherwise there wouldn't be a .99...

Also, anyone arguing that a placeholder can be discriminated is retarded.

>>3517499
forgot your troll cap, eh?

>>3517505
>But it doesn't make sense to multiply numbers with infinite precision.
The math is perfectly valid. Your objections have no rational basis - but that doesn't mean we can't fix them.

What bothers you about it?

>>3517509
>.99... does not equal 1 otherwise there wouldn't be a .99...
You're assuming that all quantities have a unique decimal representation. This is not true.

problem faggots??

>>3517509
see
>>3517197

>>3517332
HAHAHA IDIOT - STEP 3 AND FOUR OF DIGIT THEORY DOESN'T WORK.

>>3517518
The length of the limit curve of a series has no necessary relation to the length of the curves in the series.
http://qntm.org/trollpi

>>3517505
>But it doesn't make sense to multiply numbers with infinite precision.
Turns out it does. Now you know!

Here's a tip: "I don't understand how to do this" is not the same as "it does not make sense that this could be done".

>>3517509
½ does not equal 0.5 otherwise there wouldn't be a ½

Does infinity - infinity = 0 ?

>>3517550
Infinity is not a number.

>>3517535
Found the problem.
1/3 != 0.333...
It's the limit of 0.333...

>>3517562
Stop it.

>>3517550
the number of integers = ∞
the number of even integers is half the number of integers
yet the number of even integers= ∞

>>3517562
see
>>3517446

>>3517572
So 3 * 1/3 = 1
But 3 * limit of 0.333.... = limit of 0.999 = 1, I agree
But (limit of 0.999... = 1) != (0.999... = 1)
Deal with it.

>>3517562
When we say ".33...", we mean "the limit as you put more 3s after the decimal point".

To assert that "1/3 is not .33..., it's the limit as you put more 3s after the decimal point" is to deny that .33... is this limit. But it is defined to be the limit.

>>3517576
Yeah the limit is equal to 0, but 1/n never actually reaches it.
That's why the number with infinite '9' digits never reaches 1.

>>3517586
You don't have a fucking clue what "limit" means.

And 0.999... already represents infinite 9's.

>>3517586
>But (limit of 0.999... = 1) != (0.999... = 1)
.999... is defined to be the limit of .999...
They are the same thing. They are defined to be the same thing, and you cannot assert they are different without conceding that you're diverging from conventional definitions. At which point you need to a) stop talking and b) provide a new, coherent definition, starting from axioms.

>>3517602
Contradicting yourself again? Infinity is not a number, it is a limit.
0.999... IS the limit of infinite 9's.

>>3515555
240 posts, and apparently, no one is concerned

>is our children learning?

>>3517607
Yeah but when you tell people 0.999... = 1
They don't think "The more you put of '9', the more it's near 1"
They think "0.999... eventually reaches 1 and it's the same thing". Which is not.
It's never the same thing. As a function doesn't reach its asymptote.
Stay mad, chaps.

>>3517623
LIMITS NIGGER
YOU DO NOT UNDERSTAND THEM

Of course, you're not displaying troll memes, so nah, I ain't mad.

>>3517623
>They think "0.999... eventually reaches 1 and it's the same thing". Which is not.
No one thinks this.

>>3517628
>you're now displaying troll memes
lol oops

And arguing that a 0 with an infinity of 9 is also the limit of this thing is morally dubious.
There is the thing with a lot of 9 that isn't 1. And it goes toward 1 as you put more 9.

/thread

Further proof:
lim inf of 1/x = 0
Would you argue 1/x = 0 ?

>>3517676
Likewise:
lim (sum of n=1 to inf of 9/10^n) = 1
but (sum of n=1 to inf of 9/10^n) =/= 1

>>3517683
Nigger, sums to infinity are defined to be limits already. Taking the limit of a limit doesn't change its value.

>>3517702
That's what I talked about, the craziness of mathematicians.
They define an infinite sum to be the limit when the infinite doesn't even exist, and then they try to make it equal to what it will never reach.
This is the madness that allows 1 = 0.infinite9
You need something illogical to make it happen and here it is.
Fucking mathematicians.

>>3517726
No. The formal definition of "limit as x goes to infinity" does not use infinity at all. You would know this if you ever took and paid attention in a calc 1 course.

For a function f, domain is a subset of R, codomain is R,
for a Real Number C which is a limit point of dom(f),
for a Real Number L,
lim as x->+infinity of f(x) = L iff (for all e in R+) (there exists d in R) (for all x in dom(f)) (d < x implies |f(x) - L| < e)

>>3517726
>illogical
This word does not mean what you think it does.

Intuition is not logic. In fact, intuition sucks ass at being rational.

>>3517749
The thing is
If you have a god with an infinite amount of time
And you ask him to calculate sum n=1 to inf of 9/10^n, starting with 0.9 and 0.09.
He will never come to you to say he reached 1.
He will never reach it.
Even with an infinite amount of time. Because it isn't possible.
So even if you put an infinite amount of 9 after 0.
It isn't equal to 1.
The limit of the sum is 1 but that is obvious.
People are implying that an infinite of 9 decimals equals 1.
Which obviously doesn't, unless you approximate the value as the limit of the series that constructs it. And that's what you called decimal expansion, also known as mathematician craziness and laziness.

And the abuse of notation isn't 0.00..01, but 1/3 = 0.333... 1/3 is the limit of the series which contructs a number with an infinite of 3, but it isn't the number itself. It's between 0.333... and 0.333...34, and the values that separates him from 0.333... is 1/3 of the infinitesimal 0.00...001 that I talked about earlier, and that is necessary for 3*0.333... to reach 1.

>>3517894
That's great. No one is arguing that 0.999... repeating equals one because an endless process gets really close. We're arguing that it is because that's its definition, and the limit is provably equal to 1.

I know this is hard for someone new to calculus. I suspect you can't follow the symbolic logic definition given above. Take a course in calculus, and hopefully it'll make sense.

Or you're just trolling.

>>3517894
You. Do. Not. Understand. Limits.

An "infinite number of 9's" IS the limit, which IS 0.999..., which IS one.

You seem to think that infinity is a very large number, but it's not a number at all.

> 1/3 is the limit of the series which contructs a number with an infinite of 3, but it isn't the number itself.
What? Are you arguing that 1/3 is not a number?
> It's between 0.333... and 0.333...34
THAT ISN'T A NUMBER. There is no "last" three after which you can place a 4! There are infinite 3's!

>>3517894
>mathematician craziness and laziness.
Trolldar has a hit.

>>3517905
>We're arguing that it is because that's its definition
Nobody cares about the definition (except mathematicians), only about veracity.
You could argue 0! = 1 and you would be wrong, except in the crazy math society.

>>3517909
1/3 is between 0.333... infinite and 0.333...34 where you stop the 3 wherever you want.
1/3 is not 0.333 with infinite 3, unless you define infinite as the limit, which you shouldn't (mathematician craziness). You can't write it with decimals since it's irrational. But it's there.
And that's what you miss when you do 1/3 * 3 = 0.333... * 3
1/3 =/= 0.333..., it's the limit which it never reaches, it's actually another number.

>>3517954
>0! = 1 and you would be wrong, except in the crazy math society.
>1/3 is between 0.333... infinite and 0.333...34 where you stop the 3 wherever you want.
>1/3 =/= 0.333..., it's the limit which it never reaches, it's actually another number.
Hahahah, it's been fun having you troll-anon. Have a good day.

>>3517963
btw, that first one is funny because you typed it wrong, and so it's actually true when ! represents the factorial.

>>3517954
>Nobody cares about the definition (except mathematicians), only about veracity.
>You could argue 0! = 1 and you would be wrong, except in the crazy math society.

Math has no veracity. Math is true by fiat. 2+2=4 because we say so, not because of any grander reason.

We mathematicians tend to pick certain things to fiat as true because they're convenient and useful for modelling the world. 2+2=4 is true because we say so, but using Natural Numbers as a model for additions and subtractions of apples is correct and useful because the evidence says so.

In textbooks, 0^0 sometimes is defined as 1, sometimes as 0, and sometimes is explicitly said to be undefined. For ease of use, many math textbooks say that the function f(x) = 0 is not a polynomial as that makes the theorems easier to write. It's all fiat.

My high school precalc teacher many years ago once showed me a non-Euclidean geometry. It was perfectly consistent. It is just as "true" as Euclidean geometry. However, it was also effectively useless for modeling the Real World. That only means the model is not an accurate model. It says nothing about the math itself.

Im going to turn up the hur derp in here. Not only does .999... not = 1. 1 doesn't = 1. Its all a human construct the whole mathmatical language. The reason why math gets approved by other mathematicians is that people have to agree on the language. If the prevailing minds all agree that .999.. = 1 then does it make it true, even when a third grader says hey that doesn't even look kind of right. Its like when you first get introduced to math it is great because everything is so clear cut and deterministic AND usefull. Then you climb the ladder and reolize all that stuff was just agreed upon by other humans. Then you get mind rapped 1/3+1/3+1/3 = .999... =1 but that is all based off of the way we designed numerology, which is inherently flawed. HUMAN=mistakes.

>>3517974
>It's all fiat.
The AXIOMS for a given mathematical system are fiat. Their consequences are not.

>>3517979
>1 doesn't = 1
I laughed.

>>3517954
If you were working in another base, you could write 1/3 (base ten) as a whole decimal. So it's only not a number if we're writing it in base ten? The division algorithm never terminates - let's make this clear. It never terminates, not on any number whatsoever. Even those numbers on which it appears to terminate, it trails zeroes. Saying that 0.333~ does not equal 1/3rd is ridiculous, because 0.333~ is the only number that the division algorithm will produce. You can not cite another (reduced) fraction which will do so. So, I guess what, the division algorithm is wrong? We built math out of a foundation of sand? You should publish, you'll make millions.

why the fuck are people still posting in this troll thread?

>>3517981
Well, yes. I did mean that.

>>3517989
Some people like talking with trolls, I guess. Or reviewing their math.

>after a long day, go to sleep
>wake up, see this
>the only thread that was here when I went to bed

I don't know if it's good or bad that /sci/ does this.

>>3518008
it's pretty bad.

>>3517988
When you divide 10 by 3 you have 3 + a little more.
So you divide that little more by 3 and you have 0.3 + a little more.
Can't you see that it's always reaching for a little more ? It's not about repeating a number 3 ad infinitum. It's about the impossibility of representing this little more in base 10 as you said. It fails because there is this little more that it can't express. Even if you have an infinity of 3, you'll fail to reach this little more. You'll fail. You can't 1/3 into decimals. So if you have a ton of 3, an infinite of 0.333..., it's not going to be 1/3 since it still misses something. You'll have to add 0.00..003 but less than 0.00..004. And you realize it's quite not all. It's not made of an infinite of 3. It's an infinite of 3 + a little more we can't reach.
That's why 1/3 is more than 0.infinite3, and 1 is more than 0.infinite9.

>>3518008
its good

>>3518031
Luckily we don't have to represent it as an infinite process.

Let f be a function from Natural Numbers to digits, aka {0, 1, 2, ..., 9 }

A decimal expansion
a.bcdef...
Can be thought of as a function f
f(0) = a
f(1) = b
f(2) = c
f(3) = d
...
and so on

Consider f(0) = 0, and f(x) = 3 for all other x.

We can then determine the limit of this function exactly, as the results of limits are exact. The limit is equal to 1/3.

We can also demonstrate that the above function f is indeed the unique decimal expansion of the division 1/3.

>>3518031
> It's not about repeating a number 3 ad infinitum
Actually, it is. 1/3 is the same number no how many decimal places you represent explicitly.

> It's about the impossibility of representing this little more in base 10 as you said. It fails because there is this little more that it can't express.
Nah. 0.999...
The "..." represents all the 9's.

>Even if you have an infinity of 3, you'll fail to reach this little more.
Bullshit. That's the limit.

>You can't 1/3 into decimals.
Sure I can. 0.333...

>So if you have a ton of 3, an infinite of 0.333..., it's not going to be 1/3 since it still misses something.
But you just said there's infinite 3's. So tell me what is 1/3 - 0.333... = ?

>. You'll have to add 0.00..003 but less than 0.00..004.
Oh. Nevermind. You still think there's such a thing as "after" infinity.

>>3518012
I'm not actually sure. While these threads are boring and irritating in the extreme, they also show that /sci/entists can keep on arguing asinine things even while posting some quality stuff in other threads.

Also, hey I got a processorget. >>3518008

>>3518053
>Consider f(0) = 0, and f(x) = 3 for all other x.
>We can then determine the limit of this function exactly, as the results of limits are exact. The limit is equal to 1/3.
Err, I meant to say "we can determine exactly the limit of the decimal expansion represented by this function".
>We can also demonstrate that the above function f is indeed the unique decimal expansion of the division 1/3.

>>3516799

>We can prove from this that Real Numbers are a dense Field.
>Thus we can prove (for all Real Numbers A, B) (A < B or A = B or A > B).

>2011
>Thinks trichotomy is a result of being a 'dense field'

>mfw density requires an embedding in a superset
>mfw complex numbers are a 'dense field' without trichotomy
>mfw I have no face

>>3518074
You're reading into that. I never meant to imply that trichotomy follows from denseness. I was merely being terse.

>>3518054
1/3 of 10 = 1/3 of 9 + 1/3 of 1
We know how to 1/3 of 9 (3)
We don't know how to 1/3 of 1
So we say
1/3 of 1 = 1/3 of 0.9 + 1/3 of 0.1
We know how to 1/3 of 0.9
We don't know how to 1/3 of 0.1
So we start again.
Again and again.
Because we can't divide 1 by 3.
And we have that infinity, that goes toward 0.333 because we keep calculating 9/3 easily and keeping 1/3 for later. It oscillates for eternity. And with an infinity of 3, you didn't reach the goal. You failed and ended up below the target. 0.333... is below the actual 1/3 which can't be represented like that.

>>3518053
I checked decimal expansions and they're bogus, they also rely on approximating the series infinite value by its limit when n -> inf. Which is obviously wrong, think about my god example, it never reaches it in reality.

>>3518097
>I checked decimal expansions and they're bogus, they also rely on approximating the series infinite value by its limit when n -> inf. Which is obviously wrong, think about my god example, it never reaches it in reality.
I don't even know what this means.

>>3518097
>We don't know how to 1/3 of 1
Fuck you, I do.
>1/3 of 1 = 1/3 of 0.9 + 1/3 of 0.1
Sure.
>So we start again.
>Again and again.
Sure.
>Because we can't divide 1 by 3.
No, because this is what it means to divide by 3, always.


>And we have that infinity, that goes toward 0.333 because we keep calculating 9/3 easily and keeping 1/3 for later.
No. you take the limit. You haven't "finished" dividing by 3 until you take the limit. And that limit gives you 0.333...

>Which is obviously wrong, think about my god example, it never reaches it in reality.
Your mechanical definition just denies that is possible to take the limit. You're wrong.
http://en.wikipedia.org/wiki/0.999......

If you disagree, go get your Fields medal for your amazing discovery and report back.

>>3518078
I know man, I was just being a dick for fun.

If anyone would like to see a high level version of this trolling google "e e escultura".

>>3515799

Well for one thing, it doesn't work in reverse. You can't start with x=1 and get to x=.999... like that.

>>3518099
http://en.wikipedia.org/wiki/Decimal_expansion
They talk about approximation
Also
>Some authors forbid decimal representations with an infinite sequence of digits 9.
Anyway the sum goes to infinity. It relies on the mathematician craziness who believe that if the series converges vers N then its value at infinity is N, which is a theorical approximation since you can keep counting for eternity and you will never reach it.

>>3518122
Holy fuck, I'm starting to think you're not trolling. I was just playing along because I'm bored and it's mildly amusing, but are you fucking serious?

>>3518122
>Some authors forbid decimal representations with an infinite sequence of digits 9.
Wow. Only goes to show that lol-wiki.

>>3518122
>en.wikipedia.org/wiki/Decimal_expansion
>Some real numbers have two infinite decimal representations. For example, the number 1 may be equally represented by 1.000... as by 0.999...
pwned

0.999.../3=0.333...
1/3=0.333...
Just in case anyone was curious.

>>3518123
I'm talking without knowing, which is light trolling, but I'm sure that if you have an infinitely big paper and somehow write 0.333... with an infinite number of 3, it won't be the actual value of 1/3. 1/3 is between 0.3 and 0.4. Then we precise it more, 0.33 and 0.34. then more precision, ect.. It's not about adding 3, it's about adding precision, and we can't have enough precision to represent it, even with an infinity of digit. If you just think it's about having a ton of 3 then you're missing the bigger picture. 1/3 is what 0.333.. with a ton of 3 converges to but fails to reach, as 1/x converges to 0 but fails to reach it. That's why you're full of shit when you say 3*1/3 = 3*0.infinite3. You miss something. And I'm sorry but "infinite3" is not the limit except in obscure definitions; it's '3' decimals to infinity. Anyway, it just happens to be defined that 1/inf = 0 so they can calculate limits without keeping infinitesimal values around. One day they'll add notation for this. In the meantime, stay mad.

>>3518175
And that relates to a triangle all 3 sides touch each other and they are 3 equal sides. Its cyclic in a 3 sided geometrical sense. a number is a representation of a quantity it is not the actual quantity.