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I hope you all know that this is philosophical debate, not really a mathematical one.

Mathwise, the proof is fine, and it will always work, and it is as solid as 1 + 1 = 2.
Conceptually? Well have fun with that.

At 4/28/08 07:21 PM, Kuro wrote: Essentially, at an infinitely far behind the decimal place in the number, there will be a zero at the end,

If there is an end, it is not infinite.

0.999~ can not equal 1 because 0.999~ equals 0.999~. one number cannot equal another, different number.

At 4/28/08 07:26 PM, ReciprocalAnalogy wrote:

At 4/28/08 07:21 PM, Kuro wrote: Essentially, at an infinitely far behind the decimal place in the number, there will be a zero at the end,

If there is an end, it is not infinite.

But it's infinitely far along.

It's dealing with a concept which is very difficult to understand.

At 4/28/08 07:25 PM, Zerok wrote: I hope you all know that this is philosophical debate, not really a mathematical one.

Mathwise, the proof is fine, and it will always work, and it is as solid as 1 + 1 = 2.
Conceptually? Well have fun with that.

It's because it's a limit. Limits are where something will go, think of it as the destiny of a math problem.

PROBLEM SOLVED.

At 4/28/08 07:29 PM, CheeseManBlue wrote: 0.999~ can not equal 1 because 0.999~ equals 0.999~. one number cannot equal another, different number.

According to that logic 2/2 can't equal 1 because 2/2 is its own number

What's the point of arguing over this? It's not like knowing rather 0.9~ = 1 or not is going to help us in anyway. People are going to argue with each other for eternity with this question, using the same arguments over and over again.

At 4/28/08 07:28 PM, Fyndir wrote: I am aware of that, and my point was that infinity involves (very basically) the 9's never ending, I could do an entire post of the number 9 repeating until I ran out of space, and it still wouldn't be infinite.

Therefore my point still stands, no matter how many 9's there are it will never be exactly equal to 1, because it will just keep on being closer and closer without ever touching.

If you think like that then you can't believe that any given point in space exists because a point in space is an infinitely small and indeterminable area that can't be given its own space or place in existence, and yet everything around you and in you has its own point at where it exists or else nothing would.

At 4/28/08 07:40 PM, Michael wrote: According to that logic 2/2 can't equal 1 because 2/2 is its own number

No it isn't.

2/2 is an equation.

2 divided by 2 is 1.

At 4/28/08 07:28 PM, Fyndir wrote: I am aware of that, and my point was that infinity involves (very basically) the 9's never ending, I could do an entire post of the number 9 repeating until I ran out of space, and it still wouldn't be infinite.

Therefore my point still stands, no matter how many 9's there are it will never be exactly equal to 1, because it will just keep on being closer and closer without ever touching.

What you just did...
1. states infinite 9's are 9's never ending
2. gives an example of a finite number of 9's
3. uses the finite example (step 2) to say the same for an infinite number of 9's

You did it again. Used a finite amount of 9's to justify the same for an infinite amount of 9's. Infinity is not finite. .99999999 as far as I can type is not .9~ and therefore your proof is mathematically as valid as saying 5 = 2.

Infinity is a mathematical tool. Without infinity math would not work. To conceptualize infinity outside of the math (like in a physical model such as a posting area on a BBS) is to dilute the concept. At infinity, limits converge. Until infinity, they just get closer and closer. Your examples always stop before infinity because your analogy always inhabits a finite space, providing a finite number.

At 4/28/08 07:42 PM, Fyndir wrote: 0.999~/0.999~ would equal 1, just like 2/2 equals 1.

You're right 1/1 does indeed equal one.

However that doesn't mean that 0.999~ equals 1, nor does it mean that 2 equals 1. =/

Are you sure?

0^0 = 0

2^(0^0) = 2^0 = 1

1^(0^0) = 1^0 = 1

At 4/28/08 07:43 PM, Kuro wrote:

At 4/28/08 07:40 PM, Michael wrote: According to that logic 2/2 can't equal 1 because 2/2 is its own number

No it isn't.

2/2 is an equation.

2 divided by 2 is 1.

aAt 4/28/08 07:43 PM, Kuro wrote:

At 4/28/08 07:40 PM, Michael wrote: According to that logic 2/2 can't equal 1 because 2/2 is its own number

No it isn't.

2/2 is an equation.

2 divided by 2 is 1.

It's a fraction, fractions are numbers all there own, division is something you can decide to do to a fraction given the free will granted you by the heavenly father .

At 4/28/08 04:48 PM, Procrastination wrote: pi is excatly 3!

*GASP!

At 4/28/08 07:49 PM, Fyndir wrote: No matter how many 9's there are,

:o

whether you take a small finite number

True

a large finite number

True

a fucking massive finite number

True

or an infinite progression of 9's, it will never equal exactly 1. =/

False

Actually, this is how to prove .999999... is = to 1.

1/3 = .3333333333...
2/3 = .6666666666...
3/3 = .9999999999...
3/3 = 1
.9999999999... = 1

At 4/28/08 07:49 PM, Fyndir wrote: No matter how many 9's there are, whether you take a small finite number,

Not 1. I agree

a large finite number,

Not 1. I agree.

a fucking massive finite number

Not 1. I agree

or an infinite progression of 9's

Does infact equal 1. An infinite progression is not a super crazy awesomely massive finite number. It is infinite. At infinity, all 'progressions' converge on their limit. Simple fact. You're making up rules.

At 4/28/08 07:52 PM, Hellian00 wrote: Actually, this is how to prove .999999... is = to 1.

1/3 = .3333333333...
2/3 = .6666666666...
3/3 = .9999999999...
3/3 = 1
.9999999999... = 1

And this is how you prove 5 = 1

5^(0^0) = 1^(0^0)

They both arrive at the same answer and it is thus, true.

At 4/28/08 07:55 PM, Michael wrote: And this is how you prove 5 = 1

5^(0^0) = 1^(0^0)

They both arrive at the same answer and it is thus, true.

There's a funny rule in algebra that they just make you swallow. Something about 0's. Then calculus goes and explains why it doesn't work. I'm assuming you know the trick and that's why you're playing it up so much?

0.9~ = 0.9~

1 = 1

What's so difficult about that?

At 4/28/08 07:57 PM, ReciprocalAnalogy wrote: There's a funny rule in algebra that they just make you swallow. Something about 0's. Then calculus goes and explains why it doesn't work. I'm assuming you know the trick and that's why you're playing it up so much?

No idea what you're talking about

All i know is that 1^Infinity =/= 1

At 4/28/08 07:58 PM, Fyndir wrote: So are you, since infinity is just a concept.

What's your point?

Infinity is the concept that makes the rules, several that i've been using to prove that any specific number equals any other.

Please, you're a smart guy, you'd have to know what %u221E/%u221E is :(, please tell me, i'm just so confused.

At 4/28/08 07:58 PM, Fyndir wrote:

At 4/28/08 07:54 PM, ReciprocalAnalogy wrote: You're making up rules.

So are you, since infinity is just a concept.

What's your point?

Well numbers are just a concept afterall so I guess we're all wrong and we're all right. Now that we have absolute relativism out of the way...

Limits are dependant on infinity. Mathematically, as a rule, a series converges at its limit at infinity. I'm not making that up, that's the way it works. If you stop anywhere on the series and check the value, it will not equal the limit, because you haven't stopped at infinity.

At 4/28/08 08:03 PM, Fyndir wrote: Yeah, this has been a great +1 thread since I've managed to talk shit without actually doing any research and still come off as relatively serious.

Sadly it's all been for naught because in the end limits really prove why anything works.

I think copy/paste killed whatever you meant to show me. ;)

Infinity/Infinity = 1 right?

At 4/28/08 07:55 PM, Michael wrote: And this is how you prove 5 = 1

5^(0^0) = 1^(0^0)

They both arrive at the same answer and it is thus, true.

0^0 = 1, so you're saying 5^1 = 1^1, which just isn't true.

5^0 = 1^0, but you can't cancel out the "^0", because you can't get the 0 root of a number..

At 4/28/08 08:09 PM, Kuro wrote: 0^0 = 1

Nope it equals 0 since 0 times any number, no matter how many times, is still zero silly.

At 4/28/08 08:06 PM, BonusStage wrote: Infinity/Infinity = 1 right?

I don't think so. Since infinity's not actually a value.

At 4/28/08 08:11 PM, Zerok wrote:

At 4/28/08 08:06 PM, BonusStage wrote: Infinity/Infinity = 1 right?

I don't think so. Since infinity's not actually a value.

What about 0/0 then, why doesn't that work? 0 is a number.

Meh, logically, yes, .999~ can equal one. But realistically, not really.

At 4/28/08 08:18 PM, Michael wrote: What about 0/0 then, why doesn't that work? 0 is a number.

Is it?

It has a place on the number line... but what IS zero, really?
It's almost infinity expressed in a different way. Zero means nothing, but what IS "nothing"?

That's the issue with dividing by zero. What exactly are you dividing by? How many pieces should it be split into? Not one, otherwise you'd be dividing by 1, and 1 != 0. Answer? An infinite number of pieces... maybe.

Brainsplode, IMO.

At 4/28/08 08:22 PM, Zerok wrote: It has a place on the number line... but what IS zero, really?
It's almost infinity expressed in a different way. Zero means nothing, but what IS "nothing"?

Exactly, and that's why everything i've used so far to mess with people is called an "Indeterminate Form" basically they are the math equations with no answers.