Virgil wrote: > In article <firstname.lastname@example.org>, > email@example.com wrote: > >> But he claimes that the Peano-axioms 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/.
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