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From: Archimedes Plutonium on 25 Jan 2010 01:19


Nam Nguyen wrote:

>
> You've challenged few of us to come up with the definition of "finite-
> number" or else you'd go on with your ignorant babbling. So here they are,
> the definition of properties Finite(x) and Infinite(x):
>
> P(x) <-> Ey[y <= x)
> (*)P(x) <-> P(x) /\ AyEz[(y <= x) -> (z < y)]
> Finite(x) <-> ~(*)P(x)
> Infinite(x) <-> ~Finite(x)
>
> Can you quit babbling now?

Yours is deaf dumb and silent as to whether 0000....9999 is a finite-
number
or an infinite-number. And, yours obviously fails wildly for the
Hensel P-adics. Basically
you have a "order induced definition" whereas the concept of finite
and infinite is grounded
in "metric or measure" not "order".

You need to go back to the drawing board and base a definition on
"metric and absolute value" not one grounded in "order".

My precision definition of 10^500 is based on Physics of Planck Units
that no physicist
ever needs to work with any number larger than that. That is a
grounding in Measure theory
such as "absolute value" of mathematics. Did you have a chance to
study measure theory
and absolute value in school? Or did you waste your time in scribbling
symbols of logic
that never get off the ground?

P.S. Hopefully, Nam, Peter Nyikos can come to your aid and rescue.

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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