
Re: Finitely definable reals.
Posted:
Jan 14, 2013 8:23 AM


On Saturday, January 12, 2013 12:24:46 AM UTC8, WM wrote: > On 12 Jan., 02:14, Virgil <vir...@ligriv.com> wrote: > > > > > > Cantor managed to prove that there are more than countably many finite > > > > binary strings possible. Remember, the part behind a_nn of a_n is not > > > > relevant for his proof. > > > > > > Quite so, but that in no way weakens his proof. > > > > It shows a selfcontradiction by the fact that there must be an > > antidiagonal that from every entry differs at a finite place. But if > > the list is complete with respect to all finite binary strings, this > > is obviously impossible. > > > > Regards, WM
I've been thinking about this assertion of your and beg to differ. The decimal expansion of 1/3 only differs from all other reals at the infinite. It takes the infinite to make it 1/3. When one multiplies a number by 10 one moves the decimal place one position to the right. Only the infinite decimal expansion will do to restore the fraction. Any finite expansion will have a delta from 1/3.

