Re: Cardinality of Set of Computable Numbers?

From: |-|erc (trymyform_at_wwwadamskingdom.com)
Date: 12/30/03 

Date: Tue, 30 Dec 2003 15:55:15 +1000

          ----------------------------- <^> <(·¿·)> <^> -----------------------------

"Russell Easterly" <logiclab@comcast.net> wrote
>
> Saying x has an infinite number of 1's is overkill.
> I only need to show that x is longer than any string in S.

ok by 'any' here you mean all, not exists one string.
but this is trivial, just order S and add one more element.

its a strange way to define a new element.

N <-bijection-> S <-bijection-> X <-element of X not in S

> I don't have to assume x has infinite length.
> x is exactly one 1 longer than some finite string of 1's in S.
> x must have a finite string of 1's.
>

it has to be longer than the *largest* string in S
S is almost identical to X

>
> x represents a relatively "small" natural number.
> For example, x=RM(i) and i >> |x|.
> Are you sure you want me to post x?
>

Noone can follow the proof without.

Haven't you just proven all finite lists are incomplete?

Herc

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