On 2010-06-21, Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote: > "Tim Little" <firstname.lastname@example.org> wrote in message > I do understand that. But I don't actually ask for a "finite algorithm" in > my proof, I only require that I am provided a purported list of all > comptuable Reals.
Later in the proof, you claim that the antidiagonal real is computable. In other words, that there exists a finite algorithm for computing it.
> Yes, in practice, this means that each item is specified by a finite > algorithm, but so what? I ask for a purported list of all computable Reals > and show there is at least one missing.
At least one *what* missing? A real? Fine - Cantor's proof shows that there is a missing real. What's that? You want the antidiagonal to be a *computable* real? Well, then - you are required to show that there always exists a finite algorithm to compute it, and that is not present in Cantor's proof.
So your modified "proof" is either invalid, or you must include significant amounts of material not present in Cantor's proof.
As is well-known to competent mathematicians and computer scientists, no amount of material will make it valid, as the modified "theorem" is simply false. It is *not true* that any list of computable reals has a computable antidiagonal.