Date: Jan 27, 2013 1:33 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: ZFC and God
On 27 Jan., 19:21, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:

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

> > On 27 Jan., 18:44, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:

>

> >> Anyway, you haven't proved that there is a function

>

> >> f:{1,...,k} -> {0,...,9}

>

> >> as required by *your* definition of terminating decimal, so you have

> >> not shown that 0.777... is a terminating decimal.

>

> > You are wrong. Can't you understand? All natural numbers are finite.

> > Why the heck should I define a single k?

>

> Because, of course, you accepted 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.

I did not fix k but only assumed that it is a natural number.

>

> Thus, if you claim that 0.777... has a terminating representation,

> then you must show that there is a natural number k and a function f

> as above such that

>

> 0.777... = sum_i=1^k f(i) * 10^-i.

>

> Else, you have no cause to claim that 0.777... has a terminating

> decimal representation.

>

You have no cause to claim the contrary, since there is no index

(natural number) infinitely many counts away from the decimal point.

>

> > This is the definition that I agreed to.

>

> Frankly, I'm a bit stunned that you're arguing that 7/9 has a

> terminating decimal representation, but as long as you're claiming so,

> then you need to stick to the definition we've agreed on.

I am not claiming that 7/9 ot 1/3 or sqrt(2) have decimal

representations at all.

Just the contrary. But I am claiming that all decimal representations

that exist in the domain of terminating decimals are terminating, in

particular the diagonal of a Cantor-list, as long as we work in the

domain of terminating decimal representations.

If you insist in a non-terminating one, please show it!

Regards, WM