Re: WELL WHICH IS IT... ?

stephen_at_nomail.com
Date: 01/21/05 

Date: 21 Jan 2005 06:48:16 GMT

In sci.math The Ghost In The Machine <ewill@sirius.athghost7038suus.net> wrote:
: In sci.logic, Will Twentyman
: <wtwentyman@read.my.sig>
: wrote
: on Thu, 20 Jan 2005 22:20:37 -0500
:> So, apparently Ghost and I interpretted the above differently. I
:> interpretted it as "Given the list of computables, and a real number X,
:> X can have all its digits as a single entry on the list, but not be on
:> the list."
:>
:> With that reading, it is equivalent to "Given the list of computables,
:> and a real number X, X can be on the list, but not be on the list,"
:> which is obviously false.
:>
:> I'm not sure how Ghost read it.
:>

: Hmm....well, if one takes my favorite class TX_10, then it
: is clear that all of pi's finite prefixes are within TX_10,
: but pi, being irrational, is not.

: Or, one can take a constant such as Chaitin's Omega.
: This constant is a perfectly good real number, but is
: not computable, therefore cannot be on any list of computables.
: However, all of its prefixes easily can be (since one way
: of "computing" a finite sequence is simply to recite it).

Of course, even though all of the prefixes of Chaitin's Omega
will appear on a list of computables we cannot actually determine
that they are prefixes of Chaitin's Omega.

Stephen

Relevant Pages

  • Re: WELL WHICH IS IT... ?
    ... apparently Ghost and I interpretted the above differently. ... :> interpretted it as "Given the list of computables, and a real number X, ... is clear that all of pi's finite prefixes are within TX_10, ... even though all of the prefixes of Chaitin's Omega ...
    (sci.logic)
  • Re: WELL WHICH IS IT... ?
    ... apparently Ghost and I interpretted the above differently. ... :> interpretted it as "Given the list of computables, and a real number X, ... is clear that all of pi's finite prefixes are within TX_10, ... even though all of the prefixes of Chaitin's Omega ...
    (comp.theory)
  • Re: WELL WHICH IS IT... ?
    ... even though all of the prefixes of Chaitin's Omega ... >>will appear on a list of computables we cannot actually determine ... For any n there is a TM that computes the first n digits (if that's what ...
    (comp.theory)
  • Re: WELL WHICH IS IT... ?
    ... even though all of the prefixes of Chaitin's Omega ... >>will appear on a list of computables we cannot actually determine ... For any n there is a TM that computes the first n digits (if that's what ...
    (sci.math)
  • Re: WELL WHICH IS IT... ?
    ... even though all of the prefixes of Chaitin's Omega ... >>will appear on a list of computables we cannot actually determine ... For any n there is a TM that computes the first n digits (if that's what ...
    (sci.logic)
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