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

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Posts: 1,968
Registered: 12/4/12
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 <> wrote:
>> On 12/11/2012 12:55 AM, WM wrote:

>>> On 10 Dez., 21:03, fom <> 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.


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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