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