Date: Nov 21, 2012 12:57 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 154: Consistency Proof!

On 21 Nov., 18:43, William Hughes <wpihug...@gmail.com> wrote:
> On Nov 21, 1:20 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

> Nope.  The limit of the set of digits to the left of the decimal
> point is not a set of digits to the right of the decimal.


Of course it is not, but it does not prohibit that there are digits on
the right.

> If we change the limit to the set of digits to the left or right of
> the decimal point we still get {}.  {} is not a real number
> and does not have a reciprocal.


We cannot conclude from set theory that the digits on the right of the
decimal point vanish.
>
> > 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!

>
> Piffle. You really know nothing about limits do you.


In my book on analysis I write: a sequence may have many accumulation
points, If there is only one accumulation point, we call it the limit
of the sequence. (But I did not invent that definition.)
>
> > 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.

>
> Piffle.


A good argument. Possibly your last one.
>
> > Or we can find some
> > restrictions in this way.

>
> Possibly, but we need more than handwaving.


Is the limit { } of the set of digits based upon handwawing or is it
the only possible result of set theory? If the latter is true: Do you
agree that we can state: Set theory is not suitable to determine
restrictions for limits of sequences?

Regards, WM