Date: Nov 29, 2012 4:49 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 162
On 29 Nov., 19:12, mstem...@walkabout.empros.com (Michael Stemper)

wrote:

> In article <c89b62f0-d926-4b1b-a0ae-8d899d76f...@n8g2000vbb.googlegroups.com>, WM <mueck...@rz.fh-augsburg.de> writes:

>

> >On 29 Nov., 14:27, mstem...@walkabout.empros.com (Michael Stemper) wrote:

> >> In article <54e3fdd3-12f9-449e-8d84-ef2782e34...@a15g2000vbf.googlegroups.com>, WM <mueck...@rz.fh-augsburg.de> writes:

> >> >On 28 Nov., 19:20, mstem...@walkabout.empros.com (Michael Stemper) wrote:

> >> >> >Have you meanwhile convinced yourself that analysis is capable

> >> >> >expanding infinity

>

> >> >> "Expanding infinity"? What on Earth is that supposed to mean? In math,

> >> >> one is supposed to define their terms.

>

> >> >An expansion of a number is a power series giving its value.

>

> >> But, there is no such number as "infinity", so your words are still

> >> gibberish.

>

> >In set theory, there is such a number.

>

> Repeating a lie does not make it true. Set theory (at least ZF) does not

> have a number called "infinity".

There the number is called omega or aleph_0. That's but another name

for completed infinity.

>

> > In analysis there is such an

> >improper limit,

>

> And the reason that it's called an "improper limit" is because limits

> are properly numbers, and it's not a number.

Not in anaysis. Therefore I said improper limit.

>

> > an element of the extended reals.

>

> I've not studied the extended reals. I am aware that oo is an element of

> them. But, is it called a "number" in that case?

It is not of interest how it is called. But if some one calls it a

number, like Cantor who even talked about integers (ganze Zahl) then

it is called a number.

Regards, WM