Re: sketch of PROOF OF COUNTABLE REALS

From: |-|erc (h_at_r.c)
Date: 02/02/05 

Date: Wed, 2 Feb 2005 17:55:17 +1000

<rupertmccallum@yahoo.com> wrote in
> I thought you were putting forth the list of computable reals as your
> countable list of all real numbers. What list are you putting forward?
> What does "representable" mean?

Given (*), all well defined formula can be expressed in a single finite alphabet
and are countable.

Computable reals are a subset of this list, as

"UTM( 123, digit) mod 10" is some sentence
"UTM( 124, digit) mod 10" is some sentence

Not only are all the computable reals covered UTM(n e N, ..) but

"antidiag(UTM(n e N, digit) mod 10)" is also a real that it counts.

Herc

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