( A = (Set = (2*A))) = (Set = (2*A))

[yesicanread]

Please delete this thread.

[arildno]

How brilliantly perceptive you are!

[Russell E. Rierson]

( A = (Set = (2*A))) = (Set = (2*A))

I'm thinking three joined right angles.

Do you see what I'm talking about ? Or gibberish, jibberish.



A metric space (M, d) is a set M equipped with a function

d : M × M → R satisfying the following axioms for all x, y, and z in M:

d(x, y) ≥ 0

d(x, x) = 0

if d(x, y) = 0 then x = y (identity of indiscernibles)


d(x, y) = d(y, x) (symmetry)

d(x, z) ≤ d(x, y) + d(y, z) (triangle inequality)

I find the triangle inequality to be an excellent axiom!


A metric field can be defined by the primary substratum of events. Thus the intrinsic geometrical structure of spacetime is predicated on the pseudo-Riemannian spaces via the affine relationships — all physical events are fully reducible to manifestations of the substratum i. e. the metric field.


A covering map is a continuous surjective map p : C → X, with C and X being topological spaces, which has the following property: to every x in X there exists an open neighborhood U such that p^ -1(U) is a union of mutually disjoint open sets S_i (where i ranges over some index set I) such that p restricted to S_i yields a homeomorphism from S_i to U for every i in I.


Basically, a collection of subsets of a given space is a cover (or covering) of that space if the union of the collection is the whole space. Also, a space is "countably compact" if every countable open cover has a finite subcover.

A cover K is a refinement of a cover L if every member of K is a subset of some member of L.


Let's assume we are working in a complete metric space.

If so, we are in a topological space which is a set of points with a definition of a neighborhood of a point, also with a notion of distance ala a "metric", and that in the said space, Cauchy sequences have limits, where a Cauchy sequence is defined as one such that d(x_n,x_m) < epsilon can be satisfied for any epsilon by specifying an N such that n,m > N. So we are probably talking about compact spaces, or compact manifolds such that a compact complete metric space is one in which all sequences have subsequences that converge.

Stochastically speaking, gravity is must be taken beyond the limits of classical reality, where the mean value of the stress energy tensor of quantum fields also has fluctuations as a source of stochastic Einsteinian vacuum equations. Such is the necessary foundation for neo-classical gravity for the viability of inflationary cosmology based on the vacuum energy dominated phase. Metric fluctuations and spacetime foams form a chaotic substrate.

[HallsofIvy]

Its gibberish because you haven't told us what A means. If A is a number then "Set = (2*A))" makes no sense (unless the word "Set" means a number rather than a set!). If A is not a number then you would have to define "(2*A)".

I don't see what right angles have to do with any of this.

(And I have no idea what metric spaces have to do with it!)

[Lama]

Hi yesicanread,

Do you mean that there is inquality between action and reaction which is realeted to Plank constant and also to Heisenberg Uncertainty Principle?

[Locrian]

I'm having trouble concentrating now. Too much noise. But I think that's right.

That made this whole post worth reading! :biggrin:

[Locrian]

Reaction does not equal 2 * A

[Gza]

I'm having trouble concentrating now. Too much noise. But I think that's right.


Yes, those voices in your head tend to get loud at times. :wink:

[ex-xian]

Since if Action = Energy * Time, within geometry Action < 2 * Action. Since a triangle defines geometry. And if action is within geometry, a line is formed. So geometry is defined by a triangle, and not just three planar, non-colinear points.
Did you and Lama go to the same high school or something?