Date: Jan 27, 2013 12:29 PM
Author: Jesse F. Hughes
Subject: Re: ZFC and God

"Jesse F. Hughes" <jesse@phiwumbda.org> writes:

> WM <mueckenh@rz.fh-augsburg.de> writes:
>
>> On 27 Jan., 15:49, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
>>
>>> >> That is, for each i in N, the i'th digit of 0.777... is defined and is
>>> >> 7.
>>>
>>> > And do you have problems to find this confirmed as possible in the
>>> > complete set of terminating decimals? Any digit or index missing?
>>>
>>> I've no idea what you mean when you ask whether I can "find this
>>> confirmed as possible".  But, for each i in N, the i'th digit of
>>> 0.777... is defined and equals 7.  Is there anything more I need to
>>> know in order to claim that it is a non-terminating decimal?
>>
>> You need to know whether this n is an element of a finite initial
>> segment of {1, 2, 3, ..., n, n+1, n+2, ...,  n^n}.
>
> [SNIP]
>
> Sorry, let's focus on the question at hand.  I fear that your response
> diverts from the issue I want clarified.  (Once again, you've
> inadvertently snipped my primary question.)
>
> By definition, 
>
>   0.777... = sum_i=1^oo 7*10^-1.

Should be

   0.777... = sum_i=1^oo 7*10^-i

of course.  Sorry for the typo.

> You claim that 0.777... has a terminating decimal representation
> (right?).
>
> You accept the following definition:
>
>    Let x be a real number in [0,1].  We say that x has a terminating
>    decimal representation iff there is a natural number k and a
>    function f:{1,...,k} -> {0,...,9} such that
>
>     x = sum_i=1^k f(i) * 10^-i.
>
> Therefore, I request a proof that there is a function 
>
>    f:{1,...,k} -> {0,...,9} 
>
> such that
>
>   sum_i=1^k f(i)*10^-i = sum_i=1^oo 7*10^-i.
>
> Unless you can prove that there is such a function, we must conclude
> you have no proof that 0.777... is terminating.
>
> Thanks much.
-- 
Jesse F. Hughes

"This is all you have, your delusions of grandeur posting on math
newsgroups." -- James S. Harris on delusions of grandeur.