Date: Jan 29, 2013 4:27 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: ZFC and God

On 28 Jan., 22:52, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:

> >> Well, you agreed to that definition.
>
> > Of course, but not as you now put it without restriction, but under
> > the proviso that every decimal is terminating. In that case for every
> > decimal the required k exists by definition.

>
> Er.  So.
>
> You accepted the definition under the assumption that every decimal is
> terminating?


I said that we are working in the terminating decimals. I let open the
question whether there might be non-terminating decimals.

>  Well, not to put to fine a point on it, but you started
> by claiming that the set of terminating decimals is countable.


Obviously true.

> Now,
> if every real has a terminating decimal representation, then...


I did not say that every real has a terminating representation.
>
> Look, you're just making my head hurt.  I really don't have any clue
> what you think you're doing here, but it is the worst impression of
> mathematical reasoning I've ever seen, and that's saying something.


As you see above you misunderstand. That what may look worse to you is
simply your wrong impression. I don't know whether you cannot
comprehend what I said.

> AGH!  You just rejected my definition and said that a decimal is
> terminating iff it is in the set of terminating decimals, and you
> define that set with reference to the definition of terminating
> decimal.
>
> Never mind.  The point remains.  The number 0.777... is not in T.


Then show it! Show a digit that lies beyond all digits of terminating
decimals.

> The number 0.777... is the usual real number, namely
>
>   0.777... = sum_i=1^oo 7 * 10^-i.
>
> Now, is that a terminating decimal or not?


Show a digit that lies beyond all digits of terminating decimals.
Or do you claim that it is impossible to distinguish terminating and
non-terminating by digits? Or do you claim that it is impossible to
work in the domain of terminating decimals?
Why can't you support your claims?

Regards, WM