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.