"Tim Little" <tim@little-possums.net> wrote in message news:slrni1qvhp.jrj.tim@soprano.little-possums.net... > 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. >
So you assert. Personally, I think that the fact that the computable Reals are not recursively enumerable is intimately related, as a set being recursively enumerable in this context basically means the same thing as there being a mapping from N to exactly that set, ie a list of elements. It is so intimately related as to being different words for the same thing.
> 2) The word you should be using instead of "recursively enumerable" > is "surjective". >
Well, recursively enumerable is a property of sets, and surjective is a property of mappings, so dunno what you are talking about.
> 3) There are plenty of recursively enumerable functions from N -> R. >
I don't dispute that.
> Please, learn how to understand mathematical proofs so that you don't > embarrass yourself further in future. >
