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Re: ZFC and God
Posted:
Jan 25, 2013 8:50 PM
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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.
--
Jesse F. Hughes
"I'm a geek hatchling." -- Quincy P. Hughes, age 7
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