Date: Jan 15, 2013 11:05 AM
Subject: Re: Finitely definable reals.
On Jan 15, 7:53 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 15 Jan., 15:32, forbisga...@gmail.com wrote:
> > Only the infinite expansion will
> > do where the termial repeating sequense is identified as above.
> It will do? It will *never* do! Never ready, that is the meaning of
> unfinished work.
> > You know this but are just playing games. You also know that some reals
> > are irrational and do not have a termial repeating sequence. Just as
> > with the rationals only the infinite expansion will equal itself--all elese
> > are approximations. For most human purposes sufficiently close approximations
> > are good enough
> and other decimal approximations do not exist. You may say, they are
> never available. Two parallels never cross each other. That is
> tantamount to "cross each other in the infinite".
> But we can state: If parallels cross each other and irrationals have
> complete decimal expansions then Cantor is right. Or better: Only in
> the reals where parallels cross each other and irrationals have
> complete decimal expansions Cantor is right.
> Regards, WM
No, there are systems, tools, and perspectives where it is right that
parallel lines meet, and don't, and that irrationals have infinite
expansions, yet the reals as Cauchy aren't sufficient, there are
systems where Newton is right, and systems where he is, yet not
sufficiently right to represent all truth.
And, Goedel proves to use that there is more than the post-Cantorian
of ZF in a theory of sets.
And, as simply noted, ZF's universe of all its sets, would be the
Russell set, and contain itself.