Re: ******** CAN ANYONE HERE DEFINE OMEGA ? ***********

From: |-|erc (H_at_r.c)
Date: 01/30/05 

Date: Sun, 30 Jan 2005 13:04:49 +1000

<rupertmccallum@yahoo.com> wrote in message >
> What's the obvious flaw?
>

Omega doesn't converge, it equals oo.

sum (p halts) 2^-|p|

This is adapted from

sum (x has property y) 2^-x

Which always converges, some subset of this sequence,

1/2 + 1/4 + 1/8...

but Omega sums over the MUCH LARGER 1/ (2 ^ size(p))

since size(p) = floor(log(p))

It should be sum (p halts) 2^ -2|p|

then the sum is adjusted to converge. see "Herc defines HOLY GRAIL"

Herc

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