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Topic: fom - 01 - preface
Replies: 18   Last Post: Dec 12, 2012 3:34 PM

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fom

Posts: 1,968
Registered: 12/4/12
Re: fom - 01 - preface
Posted: Dec 10, 2012 3:03 PM
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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.











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