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From: Archimedes Plutonium on 21 Feb 2010 01:18

Alright, let me go through that again, to get it firm in mind.

So I define finite as 10^500, and beyond is infinite.

Now I take 9999......999999 as the largest infinite number and I take
10000.....00000 as 10% of 99999.....9999+1

Now I define Exponentiation and Root of infinite-numbers such that
10^500 is the successive 10^500 square root of 10000.....00000.

So the first root of 10000.....000000 is 00000.....00100....0000000
where the "1" digit is 1/2 of the place value rightwards of the
initial number
the second root is 00000.....0001000....0000 where the "1" digit is
1/4 of the way rightwards of the initial number etc etc.

For example
starting with 100000000000000000000 (10^20)
then the square root is 000000000010000000000 (10^10)
successive square root is 000000000000000100000 (10^5)
etc etc

So in this fashion, I suspect I can define place-value of Infinite-
Integers
by defining Finite boundary and then imposing that definition on the
number 10000000......00000 by saying that 10^500 is begot by
successive
square roots 10^500 times. Such as the number 10^5 is begot by three
successive square roots of 10^20.

What is good about this program is that I can define place-value upon
infinite integers and using the definition of precision finite number
boundary.

This program is akin to the natural program of elliptic geometry that
has its own
finite discipline placed on infinite numbers in that one
circumnavigation is the finite
boundary and where repeated circumnavigations are going to infinity
but always the
case that we merely walk over the previous first circumnavigation. So
that we can
say the transits go to infinity but that each new revolution is just
walking on old finite
ground.


Archimedes Plutonium
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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