In <virgil-2FC1D7.13530210122012@BIGNEWS.USENETMONSTER.COM>, on 12/10/2012 at 01:53 PM, Virgil <firstname.lastname@example.org> said:
>In order to define the product of a real number times a >transfinite, the definition must hold for all reals and all >transfinites.
There's a more fundamental problem; she/he/it is conflating cardinals, ordinals and elements of various algebraic systems. The product "2*omega" has nothing to do with integers, reals or cardinals, only with ordinals. The fact that the integers imbed naturally into the reals, cardinals and ordinals does not make them interchangeable.
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