wrote:
Dik Winter wrote:

...
Another question: do some of the "more points" disappear, say in
5-adics when we apply other powers and not confined to just the 5th
power. So that applying other powers we end up with only the ...000,
....0001 and idempotents and no other points of convergence?

I thought I already had answered that. In the p-adics whenever you use
any power other than p you will find there are numbers that do *not*
converge, except when that power is of the form p^k for any integer k.


Basically
I am asking if we apply all powers to a p-adic the only points of
convergence are ...000, ...001 and idempotents. Is that true?

I do not think it even does make sense. How do you *apply* all powers
to a p-adic? If you start with squaring and wait until convergence
is there you will never finish it for some numbers. So you must mean
something else. Moreover, in the p-adics the only idempotents are 0
and 1.

And in the n-adics (n not prime or a prime power) as a corollary of
my statement above and the fact that they are a direct sum of
p_i-adics,
with different primes p_i, there is *no* number k != 1 such that
succesive powering will yield convergence in all cases.

A.P. writes:

Dik, I need to show that the Adic-Rationals with a negative sign in
front of them, similar to the negative-Reals, yields a circle that is
tangent to another circle at a point which is the Adic-Integers.

Visualize a torus that is sliced into infinite number of circles. Like
a donut cut by a knife infinitely many times leaving an infinite number
of circles. Now the hole of the torus is filled by a sphere.

So the sphere is represented by the Adic Integers as points on the
sphere surface. The points of the torus are represented by the Adic
Rationals with a negative sign.

So the sphere can be the 2-adic Integers, and the torus is the 2-adic
Rationals all with a negative sign.

Dik, does the 2-adic Rationals all with a negative sign have a
mathematical reality? Does it make any kind of sense? Of course the
torus and the torus hole filled with a sphere makes all the sense in
the world, and now where I am trying to find the native-numbers of that
torus and sphere has alot of work to do.


I am going to give an outline of a proof that our physical observable
Universe is that of the surface of Riemannian geometry such as the
lobes of atoms (lobes for p, d, f, and a sphere for s orbital).

In old times we thought this proof would come only after diligent
measurement of a large triangle to see if the angle sums was greater
than 180 degrees because in Riem geom it is greater than 180 degrees.

My proof relies on no measurement of faraway stars or galaxies for
triangles. It relies on a simple fact that the speed of light is the
fastest speed in the Universe and is a Universal Constant delivering us
Special-Relativity. By simply going on those two facts constant speed
and fastest speed, logically implies that the geometry of our
observable physical universe is the surface of a sphere or lobe which
is Riem geometry.

Only Riem geometry allows for a Universal constant speed which is the
fastest speed. Loba and Eucl geometries do not allow for this and it is
intuitively seen in that a sphere has a constant parameter of its
radius or diameter or the great-circle which translates into both the
fastest and constant. In Eucl or Loba geometries, neither of which
allow for a fastest yet constant parameter because both of these
geometries are open and infinite in parameters; only is Riem geom
closed to permit a parameter that is simultaneously the "fastest and
held constant".

Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies