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