```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 areshorter. I claim that every length n of digits is finite. That is ahuge 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 allnatural 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 didnot ahree to your definition that this must be proved by finding alast 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. Thatis nonsense. Every finite index is finite. Why should we agrre upon aspecial one?>> My interest is waning here.Probably you are too much brainwashed by matheology. It is often sothat one attempts to study something but cannot succed. That's life.Regards, WM
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