Date: Jan 25, 2013 4:38 PM
Author: Jesse F. Hughes
Subject: Re: ZFC and God

WM <mueckenh@rz.fh-augsburg.de> writes:

> On 25 Jan., 19:52, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
>> WM <mueck...@rz.fh-augsburg.de> writes:
>> >> Is t_i(i) also defined for every i in N?
>>
>> > Yes, of course, with absolute certainty.
>>
>> >> Assuming you will say yes, then I must ask:
>>
>> >> Is d(i) therefore defined for every i in N?
>>
>> > Yes, of course, with absolute certainty.
>>
>> > And nothing of that takes us out of the domain of all terminating
>> > decimals, because ;

>>
>> >> > In ZF every n in N is finite.
>>
>> > and with it every FISON.
>>
>> Well, let's not get ahead of ourselves just yet.
>>
>> You agree that, for every i in N, d(i) is defined.
>>
>> I suppose you also agree that, for every i in N, d(i) != 0 and
>> d(i) != 9, right?
>>
>> Okay, so d(i) is defined for every i in N, and d(i) is non-zero and
>> not nine.
>>
>> Clearly, d is a non-terminating decimal.

>
> The set of all FISONs is not terminating. Is there a non-terminating
> FISON? No.


I'm not going to bother working through your addled analogy. Rather,
let me ask: do you disagree with the definition you snipped or not?
If not, feel free to supply your own definition.

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.

--
Jesse F. Hughes
"Mathematicians who read proofs of my results seem to basically lose
some part of themselves, like it rips at their souls, and they are no
longer quite right in the head." -- James S. Harris, Geek Cthulhu