David C. Ullrich wrote: > On Thu, 13 Jul 2006 13:52:31 -0400, Hatto von Aquitanien > <abbot@AugiaDives.hre> wrote: > > >email@example.com wrote: > > > >> In sci.math Aatu Koskensilta <firstname.lastname@example.org> wrote: > >>> Hatto von Aquitanien wrote: > >>>> For example it was recently pointed out that permutations of N result in > >>>> a demonstration that there exist uncountable bijections. > >> > >>> Really? Where can I find out more about this startling discovery? > >> > >> The above is Aquitanien's garbled interpretation of the fact > >> that there exist countable sets that are not recursively > >> enumerable. > >> > >> Stephen > >If you cannot recursively enumerate it, you can't count it. > > That depends on exactly what you mean by "count it". And it > has no relevance at all to the fact that there exist countable > non-re sets (luckily "countable" does have a precise definition).
I was taught that a set is "countable" if there exists a one-to-one correspondence between the elements of the set and the natural (counting) numbers.