Virgil
Posts:
9,012
Registered:
1/6/11


Re: Finitely definable reals.
Posted:
Jan 14, 2013 5:46 PM


In article <f69076de7f9845198e95d4563ca25208@f25g2000vby.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> wrote:
> On 14 Jan., 14:23, forbisga...@gmail.com wrote: > > 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. > > > What do you understand by this statement? > > > 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. > > In my opinion everything that in mathematics can be used to express > 1/3 as a decimal fraction is "all its finite digits". That means, only > in the infinite we obtain 1/3, but a better phrase describing "the > infinite" is simply "never". Thus WM throws out every limit process, including all of canlculus.
> We will never obtain 1/3 as a decimal.
Certainly WM won't, but calculus will.
> Alas, if Cantor was right, we must assume that "never" is a certain > point in time that can be reached and surpassed.
Only in WMytheology.
Outside of WMytheology one can have all times 1/2^n, n in N, and still have a time 0 and times greater than 0. 

