
Re: Infinity: The Story So Far
Posted:
Mar 5, 2014 4:07 PM


Virgil wrote: > In article <4cfd9bb357084ed79285e2735a4fcd85@googlegroups.com>, > mueckenh@rz.fhaugsburg.de wrote: > >> But he claimes that the Peanoaxioms supply the natural numbers of formal >> mathematics. So the natural numbers of formal mathematics are: >> 1, 10, 100, 1000, ... > > Only in wierd places like WM's wild weird world of WMytheology. > Elsewhere, the successor operation is denoted by adding one.
I don't think that is correct. The successor of x may be denoted S(x) or x' or in other ways. If S(x) is read as "multiply x by 10" and that reading is consistent with S's axioms, then that possible meaning for S is not excluded and "natural number" meaning one of "1, 10, 100, ..." is not excluded either. Russell makes a similar point in his /Introduction to mathematical philosophy/.
 Madam Life's a piece in bloom, Death goes dogging everywhere: She's the tenant of the room, He's the ruffian on the stair.

