Herc defines the HOLY GRAIL OF MATHEMATICS

From: |-|erc (H_at_r.c)
Date: 01/29/05 

Date: Sat, 29 Jan 2005 16:05:52 +1000

http://mathworld.wolfram.com/ChaitinsConstant.html
o = sum 2^(-|p|)
      (p halts)

|p| is the size in bits of program p.

Note: if ALL programs halt,

2 programs of size 1
4 programs of size 2
8 programs of size 3

omega = 1/2 + 1/2 + 1/4 + 1/4 + 1/4 + 1/4 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 ..
omega = 1 + 1 + 1 ..

If he actually meant to make a probability he should have used

Herc's Omega = sum (p halts) 2^ -2|p|

If all programs halt, you get a probability value to reflect this.

Omega = 1/4 + 1/4 + 1/16 + 1/16 + 1/16 + 1/16 + 1/64 + 1/64 ...
 = 1/2 + 1/4 + 1/8 ...
 = 1

Remember this historic moment here... www.tinyurl.com/4jpxl

Herc 

--
Throw away the chicken salad, and put a KNIFE
on the bread, and look at the sandwich as you butter it!
I don't need the chicken salad John!