fom
Posts:
1,033
Registered:
12/4/12
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Re: fom - 01 - preface
Posted:
Dec 12, 2012 11:00 AM
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On 12/12/2012 12:54 AM, WM wrote:
> On 12 Dez., 03:21, fom <fomJ...@nyms.net> wrote:
>> On 12/11/2012 12:55 AM, WM wrote:
>>
>>> On 10 Dez., 21:03, fom <fomJ...@nyms.net> wrote:
>>>> On 12/10/2012 11:57 AM, WM wrote:
>>
>> <snip>
>>
>>
>>
>>
>>
>>
>>
>>>> Yes. He did. But, Cantor's notion of a real
>>>> number was clearly found in the completion of a
>>>> Cauchy space.
>>
>>> That is completely irrelevant for the result.
>>
>>>> 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.
>>
>>> Only those which are finite.
>>
>>>> Find a different criticism of Alan's remarks
>>>> if you must. This one is incorrect.
>>
>>> So you disagree that 2 is a real number?
>>
>> Since you like quoting the Grundlagen, try
>> transcribing long detailed passages from
>> section 9
>
> I have written read an written everything Cantor wrote.
>
>> where Cantor rejects definitions
>> that conflate logical priority as you have
>> been doing.
>
> I have not been doing so. At that time there was no difference between
> reals, integers and cardinals (because Cantor did not suspect that
> there would apperar a contradiction). He just had switched from oo to
> omega. No alpphs in sight.
>>
>> That is where he calls his construction
>>
>> "... a fundamental sequence and correlate
>> it with a number b, TO BE DEFINED THROUGH
>> IT,..."
>>
>
> And those numbers are multiplied by real numbers.
wrong
the fundamental sequences ARE the real numbers
>
> [text unrelated to the topic deleted]
>>
Quite wrong.
That was the text that explained how the well-ordered
set that is referenced in 2*omega is
not described as a fundamental sequence.
Cite the sections from which
you are quoting. And quote significantly
lengthy passages so that the text is
in context.
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