Re: ******** CAN ANYONE HERE DEFINE CHAITIN'S OMEGA ? ***********

From: |-|erc (H_at_r.c)
Date: 01/31/05 

Date: Mon, 31 Jan 2005 13:19:00 +1000

"r.e.s." <r.s@ZZmindspring.com> wrote in ...
> "r.e.s." <r.s@ZZmindspring.com> wrote
> > In the thread
> > "Herc defines the HOLY GRAIL OF MATHEMATICS"
> > I'd already explained to Herc about the problems with the
> > MathWorld definition of Omega, *and* how to fix it, *and*
> > provided a reference to the paper by Calude, et al, *and*
> > explained differences between Omega and the quantity tau,
> > which is special case of your K_U.
>
> I meant to refer to the thread "Why we cannot compute omega".
>

You have no definition for a real valued Omega.

The ONLY way Omega can converge is if there is ONLY 1 program per program size.

If your number of possible programs does not increase with size, which will sum Omega to oo,
then your specification is not for a UTM as it doesn't cover all programs.

Actually, in theory, you could define a mapping from all programs to a unique program size
by padding an increasing sequence of NOP NOP NOP to every program in order.

Herc

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