
Re: Finitely definable reals.
Posted:
Jan 11, 2013 5:01 PM


On 11 Jan., 22:47, Virgil <vir...@ligriv.com> wrote: > In article > <9d94157d444e478e86a061b57259f...@f4g2000yqh.googlegroups.com>, > > WM <mueck...@rz.fhaugsburg.de> wrote: > > On 11 Jan., 10:16, Zuhair <zaljo...@gmail.com> wrote: > > > Lets say that a real r is finitely definable iff there is a predicate > > > P that is describable by a Finitary formula that is uniquely satisfied > > > by r. > > > Let's say a real r is finitely definable if every mathematician can > > understand the definition. > > That would make reals languagedependent!
Of course. If there is no language, nobody can talk about numbers. > > It may well be that a real number does not have any complete decimal > expansion, but has other definition on which people can agree
Numbers without complete decimal expansion cannot result from Cantor's list. So they are irrelevant for the present discussion.
> But even if undefined, not necessarily nonexistent.
Matheology. > > > > > and many known first order languages are of that sort and > > > they are proven to be consistent and even supportive of a proof > > > system. > > > But they can only be understood by very patient listeners. > > Which WM is not.
That was irony. Infinite languages can only be understand by people who lack any understanding.
> > In any case this kind of nonsense has nothing to do with Cantor who > > held the opinion that infinite words are nonsense. > > But Cantor also managed to prove that there are more than countably many > infinite binary strings possible
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.
> and that the standard definition of the > standard complete ordered real number field requires the existence of > more than countably many real numbers.
for people with predominantly mud in their heads.
> > And > > uncountable sets which are in bijection with N, namely the set of all > > distinguishable real numbers. > > Being in bijection with N is a special case of being countable.
I see.
Regards, WM

