Curse

Fril Estelin · Jun 06, 2008, 11:27 AM // 11:27

Quote:

Originally Posted by Rushin Roulette

true ∞

Please define this concept and its brother "false ∞"

The problem is fundamentaly in "=", not in "∞" (though this little guy is also a bit responsible). Math is a science of symbols anyway, unless you talk computational math only (it's almost a philophical point of view on life: no symbol for things that don't exist in the sense that they can be touched or looked at) you always end up in these strange situations. You should read one of Greg Egan's hard scifi story of the exploration of a fractal to get this sense of "moving out of the reality".

RotteN · Jun 06, 2008, 11:58 AM // 11:58

Quote:

Originally Posted by Rushin Roulette

to prove you wrong as you wanted with pure simple cold logic.

Mathematics only accept the rational thinking on which it is based. "pure cold logics" have nothing to do with it.

And pure from a mathematical viewpoint, 0.999∞ = 1.
There is no reason to argue over this.

Rushin Roulette · Jun 06, 2008, 02:21 PM // 14:21

As Fril Estelin stated, there are 2 versions of infinity that exist.

1. The computational version of infinity is however far the machines processign the conceptual number are able to carry on calculating (much like Pi. its a never ending number, but computers are finding more and more numbers to add on to the end as processing power increases.

1. Theoretical infinity is the human deffinition (the one I called true infinity in my last post). It states that something does not end
http://dictionary.reference.com/browse/infinity

Quote:

in·fin·i·ty
Pronunciation[in-fin-i-tee]
–noun, plural -ties.
1. the quality or state of being infinite.
2. something that is infinite.
3. infinite space, time, or quantity.
4. an infinite extent, amount, or number.
5. an indefinitely great amount or number.
6. Mathematics.
a. the assumed limit of a sequence, series, etc., that increases without bound.
b. infinite distance or an infinitely distant part of space.

If you want to prove that 0.999∞ = 1, then you have to accept the deffinition of infinity as being never ending.

Therefor 0.999∞ only = 1 if you round 0.999∞ up at one point which in itself contradicts infinity, because the number goes on and on and you cut short the number which further means

0.999∞ =/= 0.999∞

obsidian ectoplasm · Jun 06, 2008, 02:45 PM // 14:45

Wow!!!!!!!!! do you guys have an IQ of like 200? or you'se are just extremly nerdie lol

I have no idea what this sum is about...then agaion I'm only 14 lol.

Nightmares Hammer · Jun 06, 2008, 03:35 PM // 15:35

Quote:

Originally Posted by obsidian ectoplasm

Wow!!!!!!!!! do you guys have an IQ of like 200? or you'se are just extremly nerdie lol

I have no idea what this sum is about...then agaion I'm only 14 lol.

It's called the Internet!! Not so impressive...

Malice Black · Jun 06, 2008, 03:56 PM // 15:56

Quote:

Originally Posted by Rahja the Thief

It doesn't equal 1... it equals .9999 repeating. 0 =/= 0 though. Now that theorem is fun. Regrettably, I don't care enough about any of you to explain it. Have a lovely evening.

Quote of the week.

Kanyatta · Jun 06, 2008, 04:44 PM // 16:44

Quote:

Originally Posted by Fril Estelin

Please define this concept and its brother "false ∞"

I'm going to make an attempt at this, even though I will probably be wrong, since my ability to read wikipedia is not as astounding as most of you.

True ∞ = Never ending. Theoretically can never be reached.

False ∞ = What your calculator gives you when you enter "1/3" as a decimal. A calculator has to have a limit, even if it is after 2000 .3's.

Any attempt to prove 0.999∞ = 1 by "when you put it in your calculator..." could, and probably should be disregarded, since calculators are machines and do not understand the concept of infinity.

Numbers are all arbitrary anyway.

Maybe this is going in the wrong direction. Maybe 9/9 =/= 1.

Lord Sojar · Jun 07, 2008, 04:06 AM // 04:06

Ok, seriously... this has got to end.

0.999∞ isn't 1. Why? It is a line that approaches 1 but never actually reaches it; it simply just becomes such a small value, it is ASSUMED as 1 in standard mathematics. Only theory physics deals with it not being considered 1. Quantum mechanics 640, take it and learn. Until then, please don't assume to understand this type of math fully.

mrmango · Jun 07, 2008, 05:00 AM // 05:00

Quote:

Originally Posted by Rahja the Thief

Ok, seriously... this has got to end.

0.999∞ isn't 1. Why? It is a line that approaches 1 but never actually reaches it; it simply just becomes such a small value, it is ASSUMED as 1 in standard mathematics. Only theory physics deals with it not being considered 1. Quantum mechanics 640, take it and learn. Until then, please don't assume to understand this type of math fully.

Then what about the proof posted earlier?
Or this
1/3=.333inf
1/3 * 3 = 1
.333inf * 3 =.999inf
1= .999inf

**Marty Silverblade** · Jun 07, 2008, 05:48 AM // 05:48

Being mathematically minded, this made my brain explode, but heres my theory on why 0.99 doesn't equal 1.

As someone said before, 0.2-0.2=0, etc. If we apply the same logic -> 1-0.99=0.001. However, the 1 occurs after the zeroes - after infinity, which isn't possibly because infinity never ends, thus the 1 never happens. Therefore, this makes 0.99=1, although it shouldn't.

Kanyatta · Jun 07, 2008, 03:44 PM // 15:44

The only argument 1 = 0.99infinity is because infinity cannot be humanly reached, so "it has to stop somewhere" and then you have to round.

Buzzer · Jun 08, 2008, 05:01 AM // 05:01

Quote:

Originally Posted by Katsumi

They're not wrong, buzzer.

-_-
Read my post again.

Quote:

Originally Posted by Rushin Roulette

because 1 - 0.999∞ = 0.0000∞1

Really? How can you have a 1 after infinite zeroes?

Avarre · Jun 08, 2008, 06:40 AM // 06:40

Quote:

Originally Posted by mrmango

Then what about the proof posted earlier?
Or this
1/3=.333inf

This is false.

Tevash Szat · Jun 08, 2008, 07:06 AM // 07:06

This statement is quite valid. Here is a calculus proof.

You can express 0.9999.... in terms of a sequence with the summation from n=1 to n=infinity of 9(1/10)^n

That is just a simple geometric series that converges. To find the number a geometric series converges to, you use (an1 * r)/(1-r) where an1 = 9 and r = 1/10.

Thus, (9/10)/(1-1/10) => (9/10)/(9/10) = 1

I can just go on with all of the other proofs there are, but most of them are in higher math ie higher than Multivariable Calculus or Differentials and really hard to type here.

arcanemacabre · Jun 08, 2008, 08:46 AM // 08:46

Since I am horrible at math, I shall use my amazing powers of common sense!!

Two different numbers cannot possibly equal each other. Period.

So, no: .999... =/= 1

Also, how can anything infinity equal (be the same as) anything that isn't infinity? It defies two major points of common sense.

poobert · Jun 08, 2008, 09:57 AM // 09:57

A simple proof because I don't want to consult the maths grads living next door (scary people):

x=0.9999999999999......
10x=9.999999999999.......
10x-x=9 (no limit to infinity, so this is true)
9x=9
x=1

arcanemacabre · Jun 08, 2008, 10:51 AM // 10:51

Quote:

Originally Posted by poobert

A simple proof because I don't want to consult the maths grads living next door (scary people):

x=0.9999999999999......
10x=9.999999999999.......
10x-x=9 (no limit to infinity, so this is true)
9x=9
x=1

As far as that goes...

Quote:

Originally Posted by t00115577

lol guys, sorry but ye are wrong

let x = .999

1x = .999
10x - 9.990
10x-1x = 9x = 9.990 - .999 = 8.991
8.991 / 9 = .999

therefore .999 = .999

gg

This guy brings up a good point. When you multiply something by 10, you move the decimal to the right, no? Which would mean that the "infinite" 9s "end" with a 0 as they are pushed across the decimal, making the number still not equal (in this case, to 10).

But, that is impossible, right? Infinity has no "end." So, where does the extra digit come from and where does it go? Or is this one of those times that mathematics and reality just don't get along?

Kanyatta · Jun 08, 2008, 03:29 PM // 15:29

Quote:

Originally Posted by poobert

x=0.9999999999999......
10x=9.999999999999.......
10x-x=9 (no limit to infinity, so this is true)
9x=9
x=1

Do I win?

poobert · Jun 08, 2008, 04:01 PM // 16:01

arcanemacabre, this is for you, enjoy:

basically and decimal is the sum of each digit, which says that for any infinite decimal:

0.mi... = n/i=0 SUM (n->infinity, i->infinity) mi/10^n

where m is a sequence(i) of numbers

Hence simplified for 0.999 rec. = SUM (n->infinity) 9/10^n

Therefore, LIM (x->infinity) xSUM (n->1) 9/10^n, which gives you LIM (x->infinity) 1- 1/10^x = 1

where LIM (x->infinity) 1/10^x=0

The last statement is the one that you are worried about, but it holds true assuming that our axioms are correct, which you are free to debate..... just not with me :P

*edit* I think it is called Eudoxus axiom... wikipedea it or something

Avarre · Jun 08, 2008, 04:31 PM // 16:31

Quote:

Originally Posted by Kanyatta

Do I win?

UHOH GUYS HE DIVIDED BY ZERO

Quote:

Originally Posted by arcanemacabre

But, that is impossible, right? Infinity has no "end." So, where does the extra digit come from and where does it go? Or is this one of those times that mathematics and reality just don't get along?

Pretty sure you can't just ignore the final place if you want to go through that equation. 0.999∞ is theoretical; in theory you can divide by zero, but math does not work that way.