"Tim Little" <firstname.lastname@example.org> wrote in message news:email@example.com... > 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)." >
That's not how Cantor's proof starts.
It starts with a list of Real numbers where the nth digit of the nth term is known for all n.
> You can continue the proof from here if you like. >
Or, I could use exactly the same logic as used by Cantor. Indeed, if I want to prove that Cantor's proof does not in of itself prove that Reals are uncountable, I have to follow his proof exactly. Which is what I have done.