Date: Nov 21, 2012 12:20 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 154: Consistency Proof!

On 21 Nov., 17:41, William Hughes <wpihug...@gmail.com> wrote:
> On Nov 21, 12:00 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>

> > On 21 Nov., 16:54, William Hughes <wpihug...@gmail.com> wrote:
>
> <snip>
>

> > > The limit is {}.  {} is not a real number.  {} does not have a
> > > reciprocal

>
> > But the numbers allowed by an empty set of decimal left to the point
> > has a reciprocal, namely a value larger than 1.

>
> Absolute nonsense.  There are no numbers "allowed by an empty set".
> How can a set consisting of no numbers have a reciprocal?

Not nonsense but as usual you have not understaood.
There are not numerals left of the decimal point, but there may be
numerals right of the decimal point. So there is a reciprocal of
0.abc... between 1 and oo.

But that is not so important. Important and mathematical is only this:

Every infinite sequence of real numbers either has no limit or has a
limit in the real numbers or the improper limit oo. In any case there
are never two or more limits! If existing, it can be calculated
according to Cauchy. If set theory supplies a tool, then the limit can
be calculated according to Cantor too. Or we can find some
restrictions in this way.

Here we find a funny result like that: Cauchy states, that there is a
house. Cantor says that there are no stones. WH says that there is no