Date: Jan 28, 2013 9:57 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: ZFC and God

On 28 Jan., 12:44, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> WM <mueck...@rz.fh-augsburg.de> writes:
> > On 27 Jan., 23:27, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
>
> >> >> it follows *FROM THE AGREED DEFINITION* that 0.777... has no
> >> >> terminating decimal representation.

>
> >> > 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.

>
> > Please let me know where I agreed to that definition.
> > Of course, when working in the terminating decimals, every anti-
> > diagonal is terminating.

>
> In the post with
>
> Message-ID: <06a85bef-99c1-4104-862c-27351c153ccb@f6g2000yqm.googlegroups.com>
>
> we had the following exchange:
>
> ,----
> | > Let's state the definition explicitly then:
> | >
> | >   Let x be a real number in [0,1].  We say that x has a terminating
> | >   decimal representation iff there is a natural number k and a
> | >   function f:{1,...,k} -> {0,...,9} such that
> | >
> | >    x = sum_i=1^k f(i) * 10^-i.
> | >
> | > Right?
> |
> | Right.


But you forget that we had agreed that we are working in the set F of
all terminating decimals to construct a diagonal or 0.777... . Now
find out which of the digits of 0.777... that is constructed of
numbers of F has not a finite index k.

Regards, WM