# Thread: Dimensions, sets, and Fermat's Theorem

1. ## Re: Dimensions, sets, and Fermat's Theorem

Originally Posted by grapes
Or one can simply use that imagination to have both a and b on the same number line, that refutes this post:
Doesn't refute anything, if I stipulate that you never, ever factor them into partitions....
(and thus represent independent variables, since the only common partition is then unity - a/a=1 and b/b=1

Then insert a = 1 and b = 1 into the Binomial theorem)

, but is not an integer.

This is because a and b are independent (a,b), and are therefore representable as orthogonal in two dimensions (the basis of irrational numbers being a geometric construct, mapped into the line of countable integers as an enhancement of the set of integers with a metric.... (i.e., part of the real number construct)....

For irreducible integers, a/a = b/b = 1, the relation is (1,1) for irreducible integers, providing the basis for a two dimensional vector space (and the necessity of irrational numbers not a part of the integer number line ....)

2. ## Re: Dimensions, sets, and Fermat's Theorem

Originally Posted by BuleriaChk
Doesn't refute anything, if I stipulate that you never, ever factor them into partitions....
(and thus represent independent variables, since the only common partition is then unity - a/a=1 and b/b=1

Then insert a = 1 and b = 1 into the Binomial theorem)

, but is not an integer.

This is because a and b are independent (a,b), and are therefore representable as orthogonal in two dimensions (the basis of irrational numbers being a geometric construct, mapped into the line of countable integers as an enhancement of the set of integers with a metric.... (i.e., part of the real number construct)....

even if a = b = 1, the relation is (1,1) for irreducible integers....
"This is because"?

What is "this"?

Are you saying it's always not an integer, no matter what a and b are? If that's not what you are saying, what are you saying?

3. ## Re: Dimensions, sets, and Fermat's Theorem

Originally Posted by grapes
"This is because"?

What is "this"?

Are you saying it's always not an integer, no matter what a and b are? If that's not what you are saying, what are you saying?
because a and b are independent (unique, irreducible) integers: changing a does not change b. This is only true if a and b have no common factors, and the only way to ensure this is to begin with a/a = and b/b = . Since a and b are independent, the two identities are the bases of a two dimensional vector space (,).

If a and b have common factors, then changing a would change b....

This is the foundation of Cartesian coordinates for real numbers (Newton proved that the Binomial Theorem holds for real numbers as well as positive integers)... Irrational numbers arise from mapping linear geometric objects (lines, areas, volumes) into the integer line; transcendental numbers (e.g. ) arise from mapping curved geometric objects (circles, ellipses, areas of... etc...) into (positive integer + irrational) line. etc., etc.....

4. ## Re: Dimensions, sets, and Fermat's Theorem

Originally Posted by BuleriaChk
because a and b are independent (unique, irreducible) integers: changing a does not change b. This is only true if a and b have no common factors, and the only way to ensure this is to begin with a/a = and b/b = . Since a and b are independent, the two identities are the bases of a two dimensional vector space (,).

If a and b have common factors, then changing a would change b....

This is the foundation of Cartesian coordinates for real numbers (Newton proved that the Binomial Theorem holds for real numbers as well as positive integers)... Irrational numbers arise from mapping linear geometric objects (lines, areas, volumes) into the integer line; transcendental numbers (e.g. ) arise from mapping curved geometric objects (circles, ellipses, areas of... etc...) into (positive integer + irrational) line. etc., etc.....
Originally Posted by grapes
"This is because"?

What is "this"?

Are you saying it's always not an integer, no matter what a and b are? If that's not what you are saying, what are you saying?

5. ## Re: Dimensions, sets, and Fermat's Theorem

Originally Posted by grapes
(I know you didn't ask "that", but they are questions you should be asking, so you won't have to ask the one you just did ...)
(over, and over, and over, and over, and.....)

c cannot be an integer if a and b are positive integers in Fermat's equation for n > 2.

Fermat's equation = (?) for a,b,c,n positive integers, n > 2

6. ## Re: Dimensions, sets, and Fermat's Theorem

Originally Posted by BuleriaChk
(I know you didn't ask "that", but they are questions you should be asking, so you won't have to ask the one you just did ...)
(over, and over, and over, and over, and.....)

c cannot be an integer if a and b are positive integers in Fermat's equation for n > 2.
Yes, we know that because of Wiles's proof. I ask the questions because it exposes the holes in your "proof"
Fermat's equation = (?) for a,b,c,n positive integers, n > 2

You should be able to answer those questions.

7. ## Re: Dimensions, sets, and Fermat's Theorem

Originally Posted by grapes
Yes, we know that because of Wiles's proof. I ask the questions because it exposes the holes in your "proof"

You should be able to answer those questions.
I don't know that because of Wiles' proof, and neither do you. And I have already answered these questions, over, and over, and over, and over.... There may be holes in my proof, but you haven't shown any of them.

zip point shit. Nothing...

8. ## Re: Dimensions, sets, and Fermat's Theorem

Originally Posted by BuleriaChk
I don't know that because of Wiles' proof, and neither do you. And I have already answered these questions, over, and over, and over, and over.... There may be holes in my proof, but you haven't shown any of them.

zip point shit. Nothing...
I've never asked these questions before:

"This is because"?

What is "this"?

Are you saying it's always not an integer, no matter what a and b are? If that's not what you are saying, what are you saying?

9. ## Re: Dimensions, sets, and Fermat's Theorem

Originally Posted by BuleriaChk
I don't know that because of Wiles' proof, and neither do you. And I have already answered these questions, over, and over, and over, and over.... There may be holes in my proof, but you haven't shown any of them.

zip point shit. Nothing...
Has anyone else seen your "proof"? I'm totally lost by your language. The mathematical terms are all there, but there's something bizarre about the way the sentence comes out. Is there a pdf of the "proof" from start to finish, preferably without the physics (being a number-theoretic question and all)?

10. ## Re: Dimensions, sets, and Fermat's Theorem

Originally Posted by mathnerd
Has anyone else seen your "proof"? I'm totally lost by your language. The mathematical terms are all there, but there's something bizarre about the way the sentence comes out. Is there a pdf of the "proof" from start to finish, preferably without the physics (being a number-theoretic question and all)?
Start with my pdf. Skip the physics and start where I say "1 + 1 = 2"...
Study basic Cartesian coordinate system....

( have no idea what your and grapes' level of math education is, but it can't have been much...)

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