Date: Dec 12, 2012 11:00 AM
Author: fom
Subject: Re: fom - 01 - preface
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.