On 6/15/2010 4:33 PM, WM wrote: > On 15 Jun., 21:38, stevendaryl3...@yahoo.com (Daryl McCullough) wrote: >> WM says... >> >> >> >>> On 15 Jun., 18:53, stevendaryl3...@yahoo.com (Daryl McCullough) wrote: >>>> For example, we can define a real r as follows: >> >>>> r = sum from n=0 to infinity of H(n) 2^{-n} >> >>>> where H(n) = 1 if Turing machine number n halts on input n, >>>> H(n) = 0 otherwise. >> >>>> That's definable, but it is not computable. >> >>> Anyhow it is not a definition. >> >> It certainly is. It uniquely characterizes a real number, >> so it's a definition. > > It does not. If it would, the number could be computed. > Who defines what Turing machine number n would do?
Can you say "circular argument"? It's not a number because it's not computable and that proves that all numbers are computable.
