Re: My claim on Omega's defn
From: Ralph Hartley (hartley_at_aic.nrl.navy.mil)
Date: 02/03/05
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Date: Thu, 03 Feb 2005 08:59:43 -0500
r.e.s. wrote:
> <examachine@gmail.com> (I think) wrote...
>> Now, I must make the additional claim that, within all computable
>> reals, only Omegas would be random.
> Of course you meant to say "noncomputable reals".
...
> I thought you were referring to the remarkable fact that x is a random
> r.e. real in (0,1) iff x is a Chaitin Omega.
That's much better!
At least it's not so obviously false that if someone claims it is a theorem
I might believe them long enough to look at the proof. Also, I can see how
such a proof might go, though I haven't worked it out.
There are a countable number of Omegas, and I'm pretty sure there are an
uncountable number of random non-computable reals. R.e. reals are
countable, so that works better.
Ralph Hartley
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