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Topic: fom - 01 - preface
Replies: 2   Last Post: Dec 26, 2012 10:36 AM

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 Alan Smaill Posts: 1,103 Registered: 1/29/05
Re: fom - 01 - preface
Posted: Dec 24, 2012 5:47 PM

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

> On 22 Dez., 22:54, "Ross A. Finlayson" <ross.finlay...@gmail.com>
> wrote:
>

>> "The second aspect of Cantor?s letter that is puzzling is more
>> crucial, but here the puzzle only emerges when the letter is read in
>> conjunction with his letter written to Eneström one week earlier.
>> Namely, how can Cantor embrace his unrestricted addition for linear
>> numbers while maintaining ?the linear magnitudes are thoroughly
>> completed with the known real numbers?? After all, 1 + 1 + 1 + . . .
>> (taken ? times) is not a real number!
>> Of course, he could have avoided this difficulty in any of a number of
>> ways; however, as we shall soon see, while Cantor continued to embrace
>> his unrestricted addition for linear numbers (not to mention a
>> substantial strengthening thereof), he subsequently sidestepped the
>> above problem by tacitly denying that such sums of linear numbers are
>> necessarily linear. Indeed, in his discussion containing his
>> purportedly more general proof of the impossibility of infinitesimals
>> he essentially remarks in passing that every linear number is bounded
>> above by a real number."

>
> The real numbers are his "Linearkontinuum". Linearity is the
> prerequisite for multiplication.

Please note in the post you respond to:

"Indeed, in his discussion containing his
he essentially remarks in passing that every linear number is bounded
above by a real number."

>
> Regards, WM

--
Alan Smaill

Date Subject Author
12/24/12 Alan Smaill
12/26/12 mueckenh@rz.fh-augsburg.de