```Date: Jan 24, 2013 7:56 AM
Author: Jesse F. Hughes
Subject: Re: ZFC and God

"Jesse F. Hughes" <jesse@phiwumbda.org> writes:> Yes, but let's be perfectly clear here.  What we have now is this:>>   a function t: N -> R such that, for all i in N, t(i) is a real>   number with terminating decimal representation.  We'll write this as>   t_i and we'll write t_i(j) for the j'th digit of t_i (in its>   terminating representation, which is, of course, unique).>>   Let d in R be defined by>>     d(j) = 7 if t_j(j) != 7>     d(j) = 6 if t_j(j) = 6.                           ^ Should be 7, of course. >>   Clearly, for all j, d(j) != t_j(j) and hence d != t_j for any j in>   N.>> Is this what you mean up 'til now?  So, for instance, take the obvious enumeration of finite decimalrepresentations (in [0,1), of course)0.00.10.20.30.40.50.60.70.80.90.110.12...Clearly, t_i(i) = 0 for every i, and hence d_i = 7 for every i.  Thus,d = 0.777..., which is a number without any finite decimalrepresentation.-- Jesse F. Hughes"Well, if I can get [my proof of FLT accepted], then I hopefully get abook deal down the road, and maybe I get to go on 'Oprah'."  James Harris, on the rewards of mathematical endeavours.
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