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Topic: Finitely definable reals.
Replies: 52   Last Post: Jan 18, 2013 2:37 PM

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: Finitely definable reals.
Posted: Jan 16, 2013 2:09 AM

In article
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 15 Jan., 20:13, Virgil <vir...@ligriv.com> wrote:
> > In article
> >
> >  WM <mueck...@rz.fh-augsburg.de> wrote:

> > > > For most human purposes sufficiently close
> > > > approximations
> > > > are good enough
> > > > and other decimal approximations do not exist.

> >
> > So that in WMytheology only very special rationals can have decimal
> > representations at all and no irrationals have any.
> >
> >

> I think mytheology is rather an appropriate expression for the belief
> in digits after all digits at finite places.

My standard mathematics does not include any numerals for reals having
any digits in infinite places, just in infinitely many finite places,
like the decimal representation of 1/3 as infinitely many 3's each in a
finite place following the radix mark.
> >
> > > But we can state: If parallels cross each other and irrationals have
> > > complete decimal expansions then Cantor is right.

WM can, and often does, state anything he likes, but his stating things
does not make them true, and WM is somehow never able to provide proofs
valid outside his WMytheology of what he claims goes on in his
WMytheology unless it also goes on in what WM miscalls matheology but
everyone else calls standard mathematics.
> >
> > Note that, as stated, WM's claim allows Cantor to be right regardless.

>
> Cantor is right in all instances where lines that always have the same
> distance d > 0 from each other have the distance 0.

And elsewhere, though it clearly it bugs WM that Cantor is right and WM
is wrong anywhere.
>
> Regards, WM

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