"Tim Little" <tim@little-possums.net> wrote in message news:slrni1omjv.jrj.tim@soprano.little-possums.net... > On 2010-06-19, Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote: >> If you give me a purported list of all computable Reals I can use a >> diagonal argument to form a computable Real not on the list. > > OK, here you go: define f:N->R by the method of my previous post. > That is, it is the real computed by the n'th Turing machine within the > set of Turing machines that compute a real, ordered by Godel numbering > of their specifications. The function f defines a list of real > numbers. > > Your task is to find a real not on that list, and prove that it is a > computable real. > >
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.
Cantor's proof demands that you provide the list in a form whereby the nth digit of the nth entry can be determined.
My proof has exactly the same requirement.
Cantor's proof doesn't work unless the list is explicitly provided, and nor does mine.
