In article <firstname.lastname@example.org>, Shmuel (Seymour J.) Metz <email@example.com> wrote:
> In <firstname.lastname@example.org>, on 11/02/2012 > at 05:48 AM, "Peter Webb" <webbfamilyDIEspamDie@optusnet.com.au> > said: > > >The proof moves from the assertion that there can be no list of Real > >numbers to the assertion they are not countable. These are not quite > >the same thing. There are countable sets (eg computable numbers) > >which cannot be explicitly listed. > > You are confusing constructability with existence. Cantor's results > are not about constructability. > > >Given that the inability to list a set even in principle is not > >proof that it is uncountable, how does the proof go from 'there is > >no list' to 'the set is uncountable'. > > Because the definition of uncountable is that such a list does not > exist.
Or, even more directly, countability requires that such a list does exist. --