- #1
Russell E. Rierson
- 384
- 0
x^n + y^n = z^n
x^3 + y^3 = (x+y)[x^2-xy+y^2]
A more general identity for primes p, and numbers, n:
A*B means A times B
A/B means A divided by B
+ and - , we all know...
follow the order of operations:
x^p + y^p
equals
(x+y)*[(x+y)^(p-1) + [{(x^p+y^p)/(x+y)} - (x+y)^(p-1)] ]
for all p and n >= 1
Question:
Let T be a metric space with distance function r(x,y) expressing the definitive predication that involves T with the real numbers, R. Therefore the juxtaposition of left and right hemispheres resonates in perfect accordance with the proposition that T and R are embedded simultaneously in the full structure of manifold M. Ergo we pass on to an enlargement *M of M, whereby the non-standard metric space is diffeomorphism invariant.
So if f(x) is a homeomorphism from T onto S, then for every point p in T, does f(u(p) = u(f(p)) ?
A metric space is a set of points such that for every pair of points, there is a nonnegative real number called their distance that is symmetric, and satisfies the triangle inequality, which states that the sum of the measures of any two sides of any triangle is greater than the measure of the third side. Space is then a tranformation[invariant]. Two objects with relative velocity will have a relative measure that transforms into the other. In effect, the separation does not exist in an extrinsic sense. ABC = BCA = CAB
Utilizing the generalized equation:
x^3 + y^3 = (x+y)*[(x+y)^2 - 3xy]
x^5 + y^5 = (x+y)*[(x+y)^4 -5x^3 y -5(xy)^2 -5x y^3 ]
x^7 + y^7 = (x+y)*[(x+y)^6 -7yx^5 -14x^4 y^2 -21(xy)^3 -14x^2 y^4 - 7xy^5 ]
In general, x^p + y^p = (x+y)*[(x+y)^(p-1) - p*f(x,y) ]
x^3 + y^3 = (x+y)[x^2-xy+y^2]
A more general identity for primes p, and numbers, n:
A*B means A times B
A/B means A divided by B
+ and - , we all know...
follow the order of operations:
x^p + y^p
equals
(x+y)*[(x+y)^(p-1) + [{(x^p+y^p)/(x+y)} - (x+y)^(p-1)] ]
for all p and n >= 1
Question:
Let T be a metric space with distance function r(x,y) expressing the definitive predication that involves T with the real numbers, R. Therefore the juxtaposition of left and right hemispheres resonates in perfect accordance with the proposition that T and R are embedded simultaneously in the full structure of manifold M. Ergo we pass on to an enlargement *M of M, whereby the non-standard metric space is diffeomorphism invariant.
So if f(x) is a homeomorphism from T onto S, then for every point p in T, does f(u(p) = u(f(p)) ?
A metric space is a set of points such that for every pair of points, there is a nonnegative real number called their distance that is symmetric, and satisfies the triangle inequality, which states that the sum of the measures of any two sides of any triangle is greater than the measure of the third side. Space is then a tranformation[invariant]. Two objects with relative velocity will have a relative measure that transforms into the other. In effect, the separation does not exist in an extrinsic sense. ABC = BCA = CAB
Utilizing the generalized equation:
x^3 + y^3 = (x+y)*[(x+y)^2 - 3xy]
x^5 + y^5 = (x+y)*[(x+y)^4 -5x^3 y -5(xy)^2 -5x y^3 ]
x^7 + y^7 = (x+y)*[(x+y)^6 -7yx^5 -14x^4 y^2 -21(xy)^3 -14x^2 y^4 - 7xy^5 ]
In general, x^p + y^p = (x+y)*[(x+y)^(p-1) - p*f(x,y) ]