Virgil
Posts:
4,482
Registered:
1/6/11
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Re: Finitely definable reals.
Posted:
Jan 14, 2013 5:46 PM
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In article
<f69076de-7f98-4519-8e95-d4563ca25208@f25g2000vby.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 14 Jan., 14:23, forbisga...@gmail.com wrote:
> > On Saturday, January 12, 2013 12:24:46 AM UTC-8, 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 self-contradiction 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.
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