On 2010-06-20, Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote: > Cantor's proof that Reals cannot be listed requires an explicit > list, such that the nth digit of the nth term can be determined.
No, it just requires that the nth digit of the nth term exist. It does not require that the nth digit of the nth term be computable by a finite algotihm. It does not even require that there is a finite mathematical formula defining it.
> What Cantor proved (in more modern parlance) is that there is no > recursively enumerable function from N -> R.
False on three counts:
1) Recursive enumerability has nothing to do with it.
2) The word you should be using instead of "recursively enumerable" is "surjective".
3) There are plenty of recursively enumerable functions from N -> R.
Please, learn how to understand mathematical proofs so that you don't embarrass yourself further in future.