```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 ofall terminating decimals to construct a diagonal or 0.777... . Nowfind out which of the digits of 0.777... that is constructed ofnumbers of F has not a finite index k.Regards, WM
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