Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View  
Virgil

Posts: 3,546
Registered: 6/8/11
Re: � 534 Finis
Posted: Aug 20, 2014 5:14 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article <3e1c776d-9644-4943-9530-86448864936f@googlegroups.com>,
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)



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.