# Thread: Fermat's last, and mine too.

1. ## Re: Fermat's last, and mine too.

FLT Document Updated: 03/09/2017 08:08 AM PST Addendum

Further clarification of the role of vectors in the Binomial Expansion w.r.t. Presburger arithmetic, dimension, FLT's theorem and Gödel's Theorem.

2. ## Re: Fermat's last, and mine too.

Originally Posted by emperorzelos
Can you stop with the physics already? It is irrelevant to FLT

The physics interpretation of Relativity may be irrelevant in your mind (since you may not exist), but the pure mathematics is not with respect to counting mental widgets where each widget represents the final state of an imagined widget creation process.

The RUC defines sine and cosine w.r.t. the final state, and is therefore fundamental to, uh, trigonometry, which may be a new mathematical discipline for you.

The Binomial Expansion then refers to, uh, binomials, which again may be a new mathematical discipline for you. Not to mention integer multiplication in addition to, uh, addition ...

(As opposed to the constructivist perspective in one dimension, where there is only one type of widget that doesn't interact with anything else (since no other types of widget exists)

(note: elliptic functions (as all functions) require (at least) two dimensions - two different types of widgets).

STR together with the Binomial Expansion covers all widget interactions for the case in which there are only two types of widgets. This can be expanded by the Euler conjecture to include any number of different types of widgets and any number of interactions in a polynomial expansion - computer model not withstanding, depending on the computer and the model).

But, hey, if you maintain that there is only one ring (i.e., final state), at least you can't be accused of bigamy, since you're only married to yourself ...

The proposition "There is only one type of mental widget in its final state, and that type of mental widget is me" is the ultimate self-referral sentence. .

3. ## Re: Fermat's last, and mine too.

Originally Posted by BuleriaChk
The physics interpretation of Relativity may be irrelevant in your mind (since you may not exist), but the pure mathematics is not with respect to counting mental widgets where each widget represents the final state of an imagined widget creation process.

The RUC defines sine and cosine w.r.t. the final state, and is therefore fundamental to, uh, trigonometry, which may be a new mathematical discipline for you.

The Binomial Expansion then refers to, uh, binomials, which again may be a new mathematical discipline for you. Not to mention integer multiplication in addition to, uh, addition ...

(As opposed to the constructivist perspective in one dimension, where there is only one type of widget that doesn't interact with anything else (since no other types of widget exists)

(note: elliptic functions (as all functions) require (at least) two dimensions - two different types of widgets).

STR together with the Binomial Expansion covers all widget interactions for the case in which there are only two types of widgets. This can be expanded by the Euler conjecture to include any number of different types of widgets and any number of interactions in a polynomial expansion - computer model not withstanding, depending on the computer and the model).

But, hey, if you maintain that there is only one ring (i.e., final state), at least you can't be accused of bigamy, since you're only married to yourself ...

The proposition "There is only one type of mental widget in its final state, and that type of mental widget is me" is the ultimate self-referral sentence. .
Are you so delusional now that you are starting to imagine people? That's sad.

Physics is irrelevant because we are dealing with MATHEMATICS, not physics, get it?

*The RUC defines sine and cosine w.r.t. the final state, and is therefore fundamental to, uh, trigonometry, which may be a new mathematical discipline for you.*
Nope, did it back back in 10th grade.

*The Binomial Expansion then refers to, uh, binomials, which again may be a new mathematical discipline for you. Not to mention integer multiplication in addition to, uh, addition ...*
Can you construct the integers from natural numbers? I can

Just face it, in mathematics I am superior to you, I have a masters in it and getting a Ph.D, face it, you are a loser.

4. ## Re: Fermat's last, and mine too.

Originally Posted by emperorzelos

Are you so delusional now that you are starting to imagine people? That's sad.
Physics is irrelevant because we are dealing with MATHEMATICS, not physics, get it?

Can you construct the integers from natural numbers? I can
So the existence of real people has nothing to do with physics? Or mathematics?

Interesting.... Good luck in your job search...

Can you construct the natural numbers from nothing? I can...

If there is only one ring, then you're the only one imagining the axioms...

(No matter what the value of and , the area of the RUC is always

5. ## Re: Fermat's last, and mine too.

Fermat's Theorem cannot apply to the set of all integers, because the set of all integers includes the operation of multiplication, which is absent from Fermat's forumula, but present in the Binomial Expansion.

Fermat's expression only represents that of the Presburger arithmetic (which includes addition of powers of individual integers, which are themselves integers), which is consistent and complete, but has no multiplication operation.

Goedel's theorem says that the set of integers cannot be complete unless it includes multiplication, and is only complete by the Binomial Expansion, but in that case c cannot be an integer unless a=0 or b=0 for n>2, i.e. or for n > 2 for c an integer.

QED.

6. ## Re: Fermat's last, and mine too.

Originally Posted by BuleriaChk
Fermat's Theorem cannot apply to the set of all integers, because the set of all integers includes the operation of multiplication, which is absent from Fermat's forumula, but present in the Binomial Expansion.

Fermat's expression only represents that of the Presburger arithmetic (which includes addition of powers of individual integers, which are themselves integers), which is consistent and complete, but has no multiplication operation.

Goedel's theorem says that the set of integers cannot be complete unless it includes multiplication, and is only complete by the Binomial Expansion, but in that case c cannot be an integer unless a=0 or b=0 for n>2, i.e. or for n > 2 for c an integer.

QED.
Why are you sure you understand what you're talking about? You say Presburger arithmetic (which has integers) is consistent and complete, but then you say the set of integers cannot be complete without multiplication. Never mind that that doesn't make mathematical sense, why does it make sense to you?

7. ## Re: Fermat's last, and mine too.

Originally Posted by grapes
Why are you sure you understand what you're talking about? You say Presburger arithmetic (which has integers) is consistent and complete, but then you say the set of integers cannot be complete without multiplication. Never mind that that doesn't make mathematical sense, why does it make sense to you?

Presburger Arithmetic
Please read, if you want to understand my point, rather than yours.

."Peano arithmetic, which is Presburger arithmetic augmented with multiplication, is not decidable, as a consequence of the negative answer to the Entscheidungsproblem. By Gödel's incompleteness theorem, Peano arithmetic is incomplete and its consistency is not internally provable (but see Gentzen's consistency proof)" - Wikipedia

Interesting point about Gentzen, though. I'll have to see if he includes relativistic unit circles in the analysis... I'm reading further.... I suspect that if his proposal holds, then there is a question of whether the integers can be considered a subset of the real numbers....

(The problem is one of metric density ind differential geometry, where the final state of the RUC compensates for differences in gauge by allowing c,v,t, and t' to be arbitrary for the final state that defines the unit vector for that dimension.)

8. ## Re: Fermat's last, and mine too.

Originally Posted by BuleriaChk

Presburger Arithmetic
Please read, if you want to understand my point, rather than yours.
I was trying to understand your point, that's why I posted. Maybe you should re-read your own post again, and then my post, and see if you see the same error that I pointed out.
."Peano arithmetic, which is Presburger arithmetic augmented with multiplication, is not decidable, as a consequence of the negative answer to the Entscheidungsproblem. By Gödel's incompleteness theorem, Peano arithmetic is incomplete and its consistency is not internally provable (but see Gentzen's consistency proof)" - Wikipedia

Interesting point about Gentzen, though. I'll have to see if he includes relativistic unit circles in the analysis... I'm reading further....

(The problem is one of density, where the final state of the RUC compensates for differences in gauge by allowing c,v,t, and t' to be arbitrary for the final state that defines the unit vector for that dimension.)

This has significant implications for the Jacobian of the metric tensor in GTR, if all the derivatives are only integers...

We'll see...

9. ## Re: Fermat's last, and mine too.

Originally Posted by grapes
I was trying to understand your point, that's why I posted. Maybe you should re-read your own post again, and then my post, and see if you see the same error that I pointed out.
You haven't pointed out any error whatever; you have merely raised a topic that indicates you don't understand my proof via the RUC. Nor do you understand the implication of the quote, since you don't understand Presburger vs. Peano and their relation to Godel.

The set of integers with multiplication is the Binomial Expansion. Without multiplication, the system is a set of ordinal numbers of Presburger arithmetic. If multiplication is not included, the ordinals are not integers according to Peano's axioms.

The context is one of constructivist arithmetic; the context for me is the metric that defines "distance" in terms of v,c,t,and t' as arbitrary variables over the real numbers, and defines an integer as the final state of the RUC where v=0.

If you don't understand that, you may be discussing childhood arithmetic, but you certainly aren't addressing my analysis... which involves, uh, trigonometry in the creation of the number in terms of any metric whatever via the RUC.

(I'm learning as I go along, but I am studying Wiki, not relying on my own preconceptions as gospel truth. I'm still looking for a reference to the RUC.....)

Constructivists have to use Dedekind cuts to define real numbers; I begin with real numbers (the assumption of continuity of the real plane, necessary for interaction in two dimensions with a defined gauge), and define (more than one) interacting integers... there is a difference.

Once the integers are defined in independent dimensions by the RUC's (and only then) THEN Presburger or Peano applies, depending... my intuition is that Gentzen doesn't apply to this approach, but I'll have to study further to be sure...

10. ## Re: Fermat's last, and mine too.

Originally Posted by BuleriaChk
You haven't pointed out any error whatever; you have merely raised a topic that indicates you don't understand my proof via the RUC. Nor do you understand the implication of the quote, since you don't understand Presburger vs. Peano and their relation to Godel.

The set of integers with multiplication is the Binomial Expansion. Without multiplication, the system is a set of ordinal numbers of Presburger arithmetic. If multiplication is not included, the ordinals are not integers according to Peano's axioms.

The context is one of constructivist arithmetic; the context for me is the metric that defines "distance" in terms of v,c,t,and t' as arbitrary variables over the real numbers, and defines an integer as the final state of the RUC where v=0.

If you don't understand that, you may be discussing childhood arithmetic, but you certainly aren't addressing my analysis... which involves, uh, trigonometry in the creation of the number in terms of any metric whatever via the RUC.

(I'm learning as I go along, but I am studying Wiki, not relying on my own preconceptions as gospel truth. I'm still looking for a reference to the RUC.....)
Constructivists have to use Dedekind cuts to define real numbers; I begin with real numbers (the assumption of continuity of the real plane, necessary for interaction in two dimensions with a defined gauge), and define (more than one) interacting integers... there is a difference.

Once the integers are defined in independent dimensions by the RUC's (and only then) THEN Presburger or Peano applies, depending...

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