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