Date: Jan 27, 2013 1:00 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: ZFC and God

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

>
> > 0.7 is terminating.
> > if 0.777...777 with n digits is terminating, then also 0.777...7777
> > with n+1 digits is terminating. Therefore there is no upper limit for
> > the number of digits in a terminating decimal. This fact is usually
> > denoted by "infinite" and abbreviated by "...".

>
> Are you suggesting that 0.777... is *both* an infinite and terminating
> expansion?


In my opinion infinite has only one meaning, namely potenial infinity.
The set N is potentially infinite. There is no upper threshold
although every FISON is finite. - And there is nothing else.

By the AxInf we get a second infinity, namely a set N that has A
elements, where for every n in N: A > n.

If someone believes that this axiom is better than the axiom that
there are 10 different naturals with sum 10, then he should try to
find evidence. Hitherto I have not seen eveidence provided by you that
AxInf would be useful or required.

> 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?
>
> > Note, there is another meaning of infinite, namely "actually
> > infinite". Those who adhere to that notion *in mathematics* should
> > show that it differs from "potentially infinite" *in mathematics*,
> > i.e., expressible by digits.

>
> Well, I don't understand why anyone would wish to show that.


Perhaps in order to show that matheology is not complete nonsense?

> But,
> regardless, this is beside the point.  I'm asking for a proof that
> 0.777... is terminating according to the definition of terminating
> that you agreed to.


I did this in my last posting. Please look it up there. Well as I have
it just at hand, here it is again:
0.7 is terminating.
if 0.777...777 with n digits is terminating, then also 0.777...7777
with n+1 digits is terminating. Therefore there is no upper limit for
the number of digits in a terminating decimal. This is written as
0.777...

This is the definition that I agreed to.

Regards, WM