Date: Jan 28, 2013 3:53 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: ZFC and God

On 27 Jan., 23:27, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:

> > Of course. But why should we agree on a special k? Every natural
> > number will do. So we only have to know that k is one of those natural
> > numbers that belong to FISONs. As long as we work in FISONs we cannot
> > have a non-terminating decimal.
>
> I honestly have no idea what you're trying to say here.  Why not
> simply prove that there is such a k and f?

Because every natural number is finite. Why fix one of them? I do
*not* claim that there is a k such that all terminating decimals are
shorter. I claim that every length n of digits is finite. That is a
huge difference.
>
>
>
> >> What could be more obvious than this?
>
> > Remember the Binary Tree to answer your doubts. Do you believe that
> > the set of all FISONs is definable in ZF? Is every FISON finite? Is
> > there a fixed k limiting all FISONs? No.
>
> As you said before, let's keep analogies out of this.

I don't need it. But for you it was a means to understand that all
natural numbers can appear as indices of terminating decimals.

> > Show that in your 0.777..., and in particular in the anti-diagonal of
> > a list of terminating decimals, there is an index k that does not
> > belong to a FISON {1, 2, ..., n}.
>
> Utterly irrelevant to the matter at hand.  Evidently, you don't
> understand the definition you agreed to.

I agreed to the definition that every natural number is finite. I did
not ahree to your definition that this must be proved by finding a
last one. On the contrary. That is pure nonsense.
>
> > As long as you refuse there is no reason to believe you, because
> > every index in a FISON belongs to a FISON (finite initial set or
> > sequence of natural numbers). Why do you try to deny that?
>
> Who ever denied that?

You try to find a last natural k that limits all finite indices. That
is nonsense. Every finite index is finite. Why should we agrre upon a
special one?
>
> My interest is waning here.

Probably you are too much brainwashed by matheology. It is often so
that one attempts to study something but cannot succed. That's life.

Regards, WM