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Topic: � 534 Finis
Replies: 2   Last Post: Aug 20, 2014 5:14 PM

 Virgil Posts: 10,821 Registered: 6/8/11
Re: � 534 Finis
Posted: Aug 20, 2014 5:14 PM

mueckenh@rz.fh-augsburg.de wrote:

> On Tuesday, 19 August 2014 21:07:06 UTC+2, Zeit Geist wrote:
> > On Tuesday, August 19, 2014 1:50:16 PM UTC-4, muec...@rz.fh-augsburg.de
> > wrote:
> >

> > > On Tuesday, 19 August 2014 19:06:31 UTC+2, Virgil wrote:
> >
> > >
> >
> > > > Can WM provide a proof that the set of all real numbers CAN be listed?
> >
> > >
> >
> > > Of course. Which one should not be listable?
> >
> > > Each real number that can be defined in any language is defined here in
> > > this language and binary alphabet:

> >
> > >
> >
> > > a
> >
> > > b
> >
> > > aa
> >
> > > ab
> >
> > > ba
> >
> > > bb
> >
> > > aaa
> >
> > >
> >
> > > ...
> >
> >
> >
> > Which is 0?

>
> depends on the language used. There are less than aleph_0 languages.

Since only the Engish language has been used in this posting, the
question is what in the "abc" language above correspndes to the "0" in
English?
> >
> > Which is 7?

>
> Same as above.

Same criticism as above
>
> >
> > Most importantly, if I Form a Bounded, Strictly Increasing Sequence from
> > your Above "Real Numbers" will its Least Upper Bound ALWAYS Appear in the
> > List?
> >

> If you form a sequence, then you have to give a finite definition of this
> sequence. If the sequence is converging, then its limit is defined by the
> definition of the sequence.

But every sequence which is monotone and finitely bounded necessarly
converges to a real number whether its terms can be individually defined
or not. It has a real but unknowable least upper bound.
--
Virgil
"Mit der Dummheit kampfen Gotter selbst vergebens." (Schiller)