Virgil
Posts:
4,482
Registered:
1/6/11
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Re: ZFC and God
Posted:
Jan 25, 2013 9:58 PM
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In article <87ip6kvhk1.fsf@phiwumbda.org>,
"Jesse F. Hughes" <jesse@phiwumbda.org> wrote:
> WM <mueckenh@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?
>
> 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)
>
> If x has no terminating decimal representation, then we say that x is
> non-terminating.
>
> We cannot continue unless I know what you mean by terminating decimal
> representation.
WM finds precise careful definitions far too restricting for his
maunderings in Wolkenmuekenheim, so will resist either providing one
himself or accepting anyone else's.
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