```Date: Jan 26, 2013 4:36 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: ZFC and God

On 26 Jan., 02:50, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:> WM <mueck...@rz.fh-augsburg.de> writes:> >> I'm not going to bother working through your addled analogy.>> > You need not. Just ask yourself whether or not it is possible to> > define in ZFC the set of all terminating decimal representations of> > the real numbers of the unit interval. If you think that it is not> > possible, then you should try to learn it. If you know it already,> > then we can formally restrict ourselves to working in this set until> > we discover a digit that is not defined in an element of this set.>> > Your further questions then turn out meaningless.>> I asked how you define terminating decimal representation.  How is> that meaningless?Sorry, where did you ask?Nevertheless, the answer is: A terminating decimal representation(0.d_1,d_2,..., _n)  has a finite set of indices {1, 2, ..., n} with na natural number.>> Here's the definition I suggested again.  Please tell me if you agree> with it, and if not, what definition you have in mind.>> Let x be a real number in [0,1].  We say that x has a terminating> decimal representation iff there is an f:N -> {0,...,9} such> that>>   x = sum_i f(i) * 10^-i,>> and>>   (En)(Am > n)(f(m) = 0) or (En)(Am > n)(f(m) = 9)The latter is not quite correct, because a terminating decimalrepresentation has nothing behind its last digit d_n, neither zerosnor any other digits. (But of course, we can expand every terminatingdecimal by a finite set of further decimals d_j = 0 for every j with n<j <m, m in N.)>> If x has no terminating decimal representation, then we say that x is> non-terminating.>Yes.> We cannot continue unless I know what you mean by terminating decimal> representation.Should be clear now.Regards, WM
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