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From: Archimedes Plutonium on 27 Jul 2010 01:30
This is so interesting and I see no math literature ever talking about
this idea. That we take the 268! and we know it is the "all possible
digit
arrangement of 268 digit sequence of base_268. We know it is all the
numbers between 0
and 10^536 in base_10.

All Possible Digit Arrangements as permutation or factorial. Let me
talk about the idea of All Possible Digit Arrangements as building the
sphere and pseudosphere. We have the end of
Physics at 10^536 where there is no more strong-nuclear force, and
this number is the boundary between finite and infinite. Then we have
this matrix of all the numbers as
sequence strings of 536 digits long:

000..000
000..001
000..002
..
..
..
999..998
999..999

All those strings are 536 digits long.

Now we have each string as a strip, and it is one unit wide strips,
but each strip has the same
length. Each strip has a marker and the marker is the number.

So what Geometrical Probability theory does is use the concept of
"strip". We use this to eliminate "betweenness" and we use it to
construct geometry objects. So there are 10^536 strips of equal length
and one unit wide. Now the length depends on how big of a sphere you
want to construct. If a unit diameter sphere then the length of the
strip is "pi".

Now what is fascinating about this for mathematics is that the
permutation of factorial is different from the combination of
exponents. One seeks to find the all possible arrangements
of sequences, while the other seeks to find all outcomes. They seek
different things.

And they are equal at 268! = 10^536.

So what does that mean? What I can discern, is that it means we can
build a sphere the size of Earth as sphere with all the strips of 536
digits long all 1 unit wide, but that to build the associated
pseudosphere of the same diameter as the Earth sphere, it takes only
all the strings of 268 digits long strips all 1 unit wide.

So what I take as the meaning is that in algebra/arithmetic the
permutations of 268 objects
is 268! and since it is equal to the combinations of 10^536 which
measures something different in probability theory than does 268!,
yet, although they are equal. This suggests to me that the one is the
surface building of a sphere while the other is the surface building
of the associated pseudosphere. Granted, this needs proof, and I
suspect a constructive proof
is easily given, where we actually take strips and see if one requires
268 strips whilst the other requires 536 strips.

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