Fermat's Last Theorem FUNDAMENTAL

AMERICA EARTH PROUD DAY FUNDAMENTALS

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Fermat Equations INTEGRATED relational IRRATIONAL FIELD

Fermat Equations - IRRATIONAL FIELD - ANALYTIC IMPLEMENTATION.

This material claim revised in time, or if any Mathematicin will consider important, can to join to it, in his name.
Fermat - Murgu Impossible Equations brought an Absolute Conditional
n(Xⁿ) + n(Yⁿ) =n(Zⁿ)
Do not simplyfy: Ion Murgu - Double False Redundancy Of Truth demonstrated any times simplify modify equations quality.
Then witouth any doubts for n>2 those Conditional Equations Claim for Fermat's Last Theorem as (X,Y,Z) to be all Irrationals or two of them or one. This SENT Fermat's Last Theorem in FUNDAMENTAL, but also brought the ideea for covering all Irrational Field.
Irrational Infinity seem to be more then n times Integers Infinity
Infinity Paradox

Gratitude to - AMERICA 2015 TWO FUNDAMENTALS - now we can define analytic IRRATIONAL FIELD. To understood it need to understood AMERICA EARTH PROUD DAY FUNDAMENTALS presented in first maybe 10 pages in "InfinityDivergentConjecture.pdf". For it we will define a Irrational Number by its new point of view coming from above:
An irrational number is a number that cannot evolve into an integer or rational number except only by multiple multiplications with itself.
Then , that lead us to Special Irrationals :

(ⁿ√ _n)
for n ∈ [2,∞)

and also to Orinary Irrationals :
(ⁿ√ _k)
for n ∈ [2,∞) and k Rationals or Integers ∈ (0, ∞) but k ≠ h*n ; with h integer.

For n on negative axle appear a simple aspect which will born anothers kind of irrationals.
But also very important for analytic are subunitary Irrationals which deffine for an subunitary Irrational its Complementary Relative to Unity (1 - g) where g is a subunitary Irrational.
But it can be extended to all Irrationals as (1 - k + l) where k is an irrational and l its integer part. All of it born
Ion Murgu - Euler - Murgu Equations 1=1 .
which also Certify Fermat's Last Theorem for n=2 to ∞ .

We defined all Irrational Field Analytic , but knowing Fermat's Last Theorem now is Fundamental in Science and Mathematics - we know solutions for Fermat Equations are Irrationals for n ∈ [2, ∞) - we can say:

Fermat Equations Integrated Relational Irrational Field

Fermat Equations are Xⁿ + Yⁿ = Zⁿ
to associate to those equations a linear Equations into Integers
A + B + = C (ex: 9 + 12 = 21 ) a identities
Now if consider this Identities a Fermat Equations, then X = ⁿ√ _A Y = ⁿ√ _B Z = ⁿ√ _C and function of case , one, two or all can be Irrationals. This will connect all Irrationals into Relationals Identities but also Irrationals - Integers and Irrationals - Rationals. This isn't a Big Thing , but can help any time any Logical Analytic.

Any time banality can bring any ideas! Then I will come with a banal example for n=2 but which can give you a ideea ..

To name this example:
Banal Vision for Power 2 Balance.

(√ 3 -1)(√ 3 +1)=2	... ... ..	(√ 3 -√ 2)(√ 3 +√ 2)= 1
(√ 5 -1)(√ 5 +1)=4	... ... ..	(√ 5 -√ 4)(√ 5 +√ 4)= 1
(√ 7 -1)(√ 7 +1)=6	... ...	(√ 7 -√ 6)(√ 7 +√ 6)= 1
(√ 9 -1)(√ 9 +1)=8	... ...	(√ 9 -√ 8)(√ 9 +√ 8)= 1
	... ...
(√(2n+1) -1)(√ (2n+1) +1)=2n	... ...	(√ (2n+1) -√ 2n)(√(2n+1) +√2n)= 1