```Date: Jan 27, 2013 12:29 PM
Author: Jesse F. Hughes
Subject: Re: ZFC and God

"Jesse F. Hughes" <jesse@phiwumbda.org> writes:> WM <mueckenh@rz.fh-augsburg.de> writes:>>> On 27 Jan., 15:49, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:>>>>> >> That is, for each i in N, the i'th digit of 0.777... is defined and is>>> >> 7.>>>>>> > And do you have problems to find this confirmed as possible in the>>> > complete set of terminating decimals? Any digit or index missing?>>>>>> I've no idea what you mean when you ask whether I can "find this>>> confirmed as possible".  But, for each i in N, the i'th digit of>>> 0.777... is defined and equals 7.  Is there anything more I need to>>> know in order to claim that it is a non-terminating decimal?>>>> You need to know whether this n is an element of a finite initial>> segment of {1, 2, 3, ..., n, n+1, n+2, ...,  n^n}.>> [SNIP]>> Sorry, let's focus on the question at hand.  I fear that your response> diverts from the issue I want clarified.  (Once again, you've> inadvertently snipped my primary question.)>> By definition, >>   0.777... = sum_i=1^oo 7*10^-1.Should be   0.777... = sum_i=1^oo 7*10^-iof course.  Sorry for the typo.> You claim that 0.777... has a terminating decimal representation> (right?).>> You accept the following definition:>>    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.>> Therefore, I request a proof that there is a function >>    f:{1,...,k} -> {0,...,9} >> such that>>   sum_i=1^k f(i)*10^-i = sum_i=1^oo 7*10^-i.>> Unless you can prove that there is such a function, we must conclude> you have no proof that 0.777... is terminating.>> Thanks much.-- Jesse F. Hughes"This is all you have, your delusions of grandeur posting on mathnewsgroups." -- James S. Harris on delusions of grandeur.
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