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Re: fom - 01 - preface
Posted:
Dec 24, 2012 5:47 PM
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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
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