Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.


Virgil
Posts:
9,362
Registered:
6/8/11


Re: � 534 Finis
Posted:
Aug 20, 2014 5:14 PM


In article <3e1c776d96444943953086448864936f@googlegroups.com>, mueckenh@rz.fhaugsburg.de wrote:
> On Tuesday, 19 August 2014 21:07:06 UTC+2, Zeit Geist wrote: > > On Tuesday, August 19, 2014 1:50:16 PM UTC4, muec...@rz.fhaugsburg.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)



