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Firedrake969 · 2013-01-12 22:47:18

Fermat's Last Theorem basically states x^n + y^n = z^n has no solutions for n > 2 (does n also have to be a whole number? Not sure). It's been solved recently, but puzzled people for about three centuries. Discuss.
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Some sources:
A few books I'm reading
Wikipedia
Articles on infinity
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I'm assuming that n just has to be greater than two. Therefore, I made a semi-contradiction of it.
Let x, y, and z be anything. Let n be infinity. Therefore, x^infinity + y^infinity = z^infinity. I'm pretty sure you agree that infinity > 2. By the theorem, this states that x^infinity + y^infinity = z^infinity has no integer solutions for x, y, and z together. However, x^infinity + y^infinity = z^infinity is the same as infinity + infinity = infinity. Infinity + infinity does equal infinity. QED.

Ideas supporting/contradicting this? Please be critical. wink

Last edited by Firedrake969 (2013-01-13 14:34:46)

zubblewu · 2013-01-12 22:52:29

infinity isn't a number
contradicted

Programmer_112 · 2013-01-12 23:13:35

zubblewu wrote:
infinity isn't a number
contradicted

I'll show the proof. So, infinity minus one is . . . infinity. In fact, infinity - (1x) is infinity. So is infinity/(1x). So, infinity minus infinity equals infinity, and so does infinity divided by infinity, right? Now substitute y for infinity. Y-y =y, so y=0. But y is infinity, greater than zero, so infinity is just a concept. You can also do pretty much the same with y/y =y, so y is one, which doesn't work. And, with these, infinity is both one AND zero, depending on the equation. Concept. Not number.

zubblewu · 2013-01-12 23:34:34

firedrake said "a number"
infinity is not a number

RenOkshadia3537 · 2013-01-13 03:22:32

3^3 + (-3)^3 = 0^3

Doesn't this work?

RenOkshadia3537 · 2013-01-13 03:25:49

Wait, just went to wikipedia, is stated that no POSITIVE number could satisfy the equation. Next time you should point that out hmm .

Firedrake969 · 2013-01-13 09:57:36

Infinity is greater than 3. xD

I know infinity is a concept, I just wanted to point out the flaw.

zubblewu · 2013-01-13 10:18:08

it's not a flaw if it has to be a number

Firedrake969 · 2013-01-13 10:21:46

zubblewu wrote:
it's not a flaw if it has to be a number

Where does it say it's a number? I don't want to read the whole thing again. And they used number in a generalized concept, not a precise definition.

zubblewu · 2013-01-13 10:23:07

"I'm assuming that n has to be a number."

technoguyx · 2013-01-13 11:58:24

RenOkshadia3537 wrote:
3^3 + (-3)^3 = 0^3

Doesn't this work?

3³; (-3)³ = 27

27 + 27 = 0³
54 = 0

no

zubblewu · 2013-01-13 12:11:11

-3^3 is actually -27

technoguyx · 2013-01-13 12:57:45

oh right. >.>

Well, it does, but according to the Wikipedia article about the theorem:

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c can satisfy the equation a^n + b^n = c^n for any integer value of n greater than two.

calebxy · 2013-01-13 13:06:46

Programmer_112 wrote:
zubblewu wrote:
infinity isn't a number
contradicted
I'll show the proof. So, infinity minus one is . . . infinity. In fact, infinity - (1x) is infinity. So is infinity/(1x). So, infinity minus infinity equals infinity, and so does infinity divided by infinity, right? Now substitute y for infinity. Y-y =y, so y=0. But y is infinity, greater than zero, so infinity is just a concept. You can also do pretty much the same with y/y =y, so y is one, which doesn't work. And, with these, infinity is both one AND zero, depending on the equation. Concept. Not number.

No, infinity - infinity = 0. I'll show you:

3.333... has an infinite amount of 3 on the end. But: 3.333... - 0.333... = 3, which is the same concept that's used to prove that 0.9... = 1.

Last edited by calebxy (2013-01-13 13:07:14)

Firedrake969 · 2013-01-13 14:35:45

This is about FLT, not infinity. tongue Anyways, infinity - infinity = infinity. The 0.3333... example doesn't have to do with what we're talking about.

Aidan · 2013-01-13 14:48:54

Firedrake969 wrote:
Let n be infinity.

If you've read articles on infinity, you should know that this is where the problem with your so-called "contradiction" arises. Infinity is a concept, not a number (as others have stated), so it then stands to reason that you CAN'T USE IT IN MATHEMATICAL FORMULAS

Firedrake969 wrote:
This is about FLT, not infinity. Anyways, infinity - infinity = infinity. The 0.3333... example doesn't have to do with what we're talking about.

We're discussing the problems with your proposed "contradiction." I don't see what the problem is, since you told us to "be critical"

INFINITY CAN'T BE USED IN MATHEMATICAL FORMULAS BECAUSE NOT A NUMBER

Q.E.D.

Firedrake969 · 2013-01-13 14:59:17

Ah, but infinity is used in equations. And a contradiction is a contradiction is a contradiction, no need for parenthesis. Or bold or italics, for that matter. Infinity is used in number theory quite a bit. For example, for many proofs, you'll learn that they need to prove an infinite number of cases. Therefore, they use induction reasoning.

Programmer_112 · 2013-01-13 15:58:04

Ahh. But those are the number of cases. Not the number itself. Unless you mean geometric equations over arithmetic equations, which technically approach zero, and so are slightly rounded. QED for the first time in my life. I start proofs tomorrow. *scared*

calebxy · 2013-01-13 16:20:34

Firedrake969 wrote:
Anyways, infinity - infinity = infinity. The 0.3333... example doesn't have to do with what we're talking about.

You are taking away an infinite number of 0.3s by an infinite amount of 0.3s. So you can minus infinity by infinity, which leaves you with nothing. So infinity - infinity = 0.

lalala3 · 2013-01-13 16:35:09

calebxy wrote:
Firedrake969 wrote:
Anyways, infinity - infinity = infinity. The 0.3333... example doesn't have to do with what we're talking about.
You are taking away an infinite number of 0.3s by an infinite amount of 0.3s. So you can minus infinity by infinity, which leaves you with nothing. So infinity - infinity = 0.

You're neither subtracting infinity from infinity, nor subtracting an infinite number of 0.3s from an infinite number of 0.3s. You are subtracting an infinitely continuing sequence of 3s following a decimal point. That is the distinction.

calebxy · 2013-01-13 16:46:47

lalala3 wrote:
calebxy wrote:
Firedrake969 wrote:
Anyways, infinity - infinity = infinity. The 0.3333... example doesn't have to do with what we're talking about.
You are taking away an infinite number of 0.3s by an infinite amount of 0.3s. So you can minus infinity by infinity, which leaves you with nothing. So infinity - infinity = 0.
You're neither subtracting infinity from infinity, nor subtracting an infinite number of 0.3s from an infinite number of 0.3s. You are subtracting an infinitely continuing sequence of 3s following a decimal point. That is the distinction.

Well I've never heard that before. Would you mind citing a source to back that up?

Firedrake969 · 2013-01-13 17:01:49

calebxy wrote:
lalala3 wrote:
calebxy wrote:

You are taking away an infinite number of 0.3s by an infinite amount of 0.3s. So you can minus infinity by infinity, which leaves you with nothing. So infinity - infinity = 0.
You're neither subtracting infinity from infinity, nor subtracting an infinite number of 0.3s from an infinite number of 0.3s. You are subtracting an infinitely continuing sequence of 3s following a decimal point. That is the distinction.
Well I've never heard that before. Would you mind citing a source to back that up?

Would you mind? I agree with lalala3. Don't want to type the same thing in a different format ( tongue ) but the source is common sense.

jackrulez · 2013-01-13 17:11:06

Infinity minus infinity not equaling zero and infinity divided by infinity not equaling one is silly and false. Just because something is infinitely large doesn't mean it doesn't act like any other number.

Firedrake969 · 2013-01-13 17:15:11

jackrulez wrote:
Infinity minus infinity not equaling zero and infinity divided by infinity not equaling one is silly and false. Just because something is infinitely large doesn't mean it doesn't act like any other number.

But it's not a number. xD

mythbusteranimator · 2013-01-13 17:18:55

;oo

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#1 2013-01-12 22:47:18

Fermat's Last Theorem

#2 2013-01-12 22:52:29

Re: Fermat's Last Theorem

#3 2013-01-12 23:13:35

Re: Fermat's Last Theorem

zubblewu wrote:

#4 2013-01-12 23:34:34

Re: Fermat's Last Theorem

#5 2013-01-13 03:22:32

Re: Fermat's Last Theorem

#6 2013-01-13 03:25:49

Re: Fermat's Last Theorem

#7 2013-01-13 09:57:36

Re: Fermat's Last Theorem

#8 2013-01-13 10:18:08

Re: Fermat's Last Theorem

#9 2013-01-13 10:21:46

Re: Fermat's Last Theorem

zubblewu wrote:

#10 2013-01-13 10:23:07

Re: Fermat's Last Theorem

#11 2013-01-13 11:58:24

Re: Fermat's Last Theorem

RenOkshadia3537 wrote:

#12 2013-01-13 12:11:11

Re: Fermat's Last Theorem

#13 2013-01-13 12:57:45

Re: Fermat's Last Theorem

#14 2013-01-13 13:06:46

Re: Fermat's Last Theorem

Programmer_112 wrote:

zubblewu wrote:

#15 2013-01-13 14:35:45

Re: Fermat's Last Theorem

#16 2013-01-13 14:48:54

Re: Fermat's Last Theorem

Firedrake969 wrote:

Firedrake969 wrote:

#17 2013-01-13 14:59:17

Re: Fermat's Last Theorem

#18 2013-01-13 15:58:04

Re: Fermat's Last Theorem

#19 2013-01-13 16:20:34

Re: Fermat's Last Theorem

Firedrake969 wrote:

#20 2013-01-13 16:35:09

Re: Fermat's Last Theorem

calebxy wrote:

Firedrake969 wrote:

#21 2013-01-13 16:46:47

Re: Fermat's Last Theorem

lalala3 wrote:

calebxy wrote:

Firedrake969 wrote:

#22 2013-01-13 17:01:49

Re: Fermat's Last Theorem

calebxy wrote:

lalala3 wrote:

calebxy wrote:

#23 2013-01-13 17:11:06

Re: Fermat's Last Theorem

#24 2013-01-13 17:15:11

Re: Fermat's Last Theorem

jackrulez wrote:

#25 2013-01-13 17:18:55

Re: Fermat's Last Theorem

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