"Tim Little" <email@example.com> wrote in message news:firstname.lastname@example.org... > On 2010-06-18, Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote: >> Cantor's proof does *not* demonstrate that Reals are uncountable, it >> just proves there can be no explicit enumeration of them. > > It proves that there is no enumeration of them, explicit or not. I > have no idea where you are getting this strange notion of > "explicitness". >
Because Cantor's proof requires an explicit listing. This is a very central concept.
I can form a list of sorts of all computable Reals. I can associate every Real with the TM that produces it, and list TMs in order. The trouble is that this is not an explicit list, as you cannot say exactly what number appears at each position in the list. This means Cantor's proof cannot be used, which assumes you explicitly know what number appears at every position in the list.