In article <4c19cd2c$0$316$afc38c87@news.optusnet.com.au>, "Peter Webb" <webbfamily@DIESPAMDIEoptusnet.com.au> wrote:
> Cantor's proof applied to computable numbers proves you cannot form a > computable list of computable numbers. Cantor's proof applied to Reals > proves you cannot form a computable list of Reals.
To be correct, there is no computable list of ALL of the computable numbers, even though the set of computable numbers is e countable, but there are lots of possible computable lists of computable numbers. For example, for n in {1,2,3,...}, f(n) = 1/n is a computable 'list' of computable numbers. > > The property "that you cannot form a computable list" is not the same as the > property "is uncountable". For example, computable numbers have the first > property but not the second. Cantor's proof is about what can be expressed > in a list, and not directly about uncountable sets (which don't even get > mentioned in the proof). > > > > > > > > > > - Tim
