Date: Jan 25, 2013 8:50 PM
Author: Jesse F. Hughes
Subject: Re: ZFC and God
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