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




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


WM <mueckenh@rz.fhaugsburg.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



