Date: Dec 10, 2012 3:03 PM
Author: fom
Subject: Re: fom - 01 - preface
On 12/10/2012 11:57 AM, WM wrote:

> On 10 Dez., 18:24, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:

>> WM <mueck...@rz.fh-augsburg.de> writes:

>>> On 9 Dez., 23:40, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:

>>>> WM <mueck...@rz.fh-augsburg.de> writes:

>>>>> On 8 Dez., 23:37, Virgil <vir...@ligriv.com> wrote:

>>>>>> Aleph_0 is not a length, nor an area, nor a volume.

>>

>>>>> If it was a whole number or integer, as Cantor insisted, then it could

>>>>> be used to define a length or an area or a volume etc.

>>

>>>> Cantor defined it as a cardinal number;

>>>> he did not propose any notion of multiplication of,

>>>> eg real numbers by transfinite cardinals.

>>

>>> You are badly informed.

>>

>> Then please inform me;

>> did Cantor consider 3.14159... to be a cardinal number?

>> In which of Cantor's number classes does 3.14159... fall?

>

> First you said something else, namely: "he did not propose any notion

> of multiplication of, eg real numbers by transfinite cardinals". This

> claim is wrong because 2, 3, .. are real numbers. Cantor defined

> 2*omega, 3*omega, ...

> [Grundlagen einer allgemeinen Mannigfaltigkeitslehre (Leipzig 1883)]

Yes. He did. But, Cantor's notion of a real

number was clearly found in the completion of a

Cauchy space. He found that more appealing

than Dedekind cuts. This is evident since

his topological result of nested non-empty

closed sets in a complete space is closely

related.

There are ordinal numbers in set theory given

the names of natural numbers.

Find a different criticism of Alan's remarks

if you must. This one is incorrect.