On 2010-06-19, Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote: > After all, I am trying to make my proof exactly the same as > Cantor's, but with the only difference being the word "computable" > in front of the word "Real".
If you intend your proof to be "exactly the same as Cantor's, but with the only difference being the word "computable" in front of the word "Real"", it must start with a conditional introduction. In other words, something like:
"Suppose that L is a list of computable Reals. That is, L is a function from N to R and for all n in N, there exists a Turing Machine T_n such that when provided with k as input, T_n halts and outputs the k'th decimal digit of L(n)."