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.
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)?