"Tim Little" <email@example.com> wrote in message news:firstname.lastname@example.org... > On 2010-06-19, Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote: >> You haven't specified the list. I have to guess at some of the >> entries in the list, as I don't actually know and cannot determine >> which TMs halt. > > I have explicitly specified the list (which is actually a lot more > than Cantor's proof requires). It is not my problem whether you are > incapable of determining which TM's halt. It is a well-defined > mathematical function with all the properties assumed in Cantor's > proof. >
No. Cantor's proof requires that the nth digit of the nth term can be determined.
> Likewise the following is a valid list of binary digits: f(n) = 1 if > there are infinitely many prime pairs of the form (p, p+n), f(n) = 0 > otherwise. It doesn't matter whether or not you personally know the > value of f(2), or even whether there exists an algorithm to find out: > it is still a well-defined mathematical object. > > > Are you now starting to see the difference between the term "list" (as > used in Cantor's proof) and "recursively enumerable list" (as you are > using in yours)? >
I am not using the term "recursively enumerable list" in my proof. Re-read it.
I am asking for a list in *exactly* the same way as Cantor asks for a list, excepting that it contains only computable Reals and not just any Real.