> Am Montag, 9. Dezember 2013 22:58:08 UTC+1 schrieb wpih...@gmail.com: > > On Monday, December 9, 2013 4:42:49 PM UTC-4, WM wrote:
> > > Am Montag, 9. Dezember 2013 20:13:31 UTC+1 schrieb wpih...@gmail.com:
> > > > Note that this is sufficient to show there is no constructable list L,
> > > Cantor's enumeration of the rationals is a construction.
> > True but completely irrelevant. Cantor's enumeration of the rationals > > does not contain all constructable numbers.
Since some constructable numbers are irrational, one would hope not!
> True but completely irrelevant. It is his list such that d cannot be > distinguished from many numbers by its digits.
Since every number in the list, being rational, has an eventually periodic decimal (or other base) expansion, and every irrational number, has a non-periodic expansion, sothere must be infinitely many places at which it differs from any rational.
> > It is long since time that you > > should agree there is no constructable list of constructable > > numbers.
> I know that. But that is irrelevant for my proof. I need only the list of all > rational numbers. That is constructable.
And any antidiagonal of such a list will not be rational, thus not in it. --