On 4/20/2013 1:44 PM, WM wrote: > On 20 Apr., 19:45, fom <fomJ...@nyms.net> wrote: >> >>> Mathematicians can. Dedekind was a mathematician. Dedekind could. >> >> Yes. It does depend on definitions. >> >> I will not get my copy out concerning this matter >> since I made the distinctions correctly. > > Not with respect to the inventor of that matter. >> >> However, Dedekind did not call his domains inductive >> sets. > > > Neither did I. > >> He called them simply infinite sets. >> >> It depends on the definitions. > > Not in the mathematics of Dedekind and myself. >>
It would, apparently, be appropriate to call WM a liar here, although I have heard that in German there can be some ambiguity concerning the words surrounding the translation of "definition".
Definition. A system N is said to be simply infinite when there exists a similar transformation P of N in itself such that N appears as chain of an element not contained in P(N). We call this element, which we shall denote in what follows by the symbol '1', the base-element of N and say the simply infinite system N is set in order by this transformation P.
It seems that Dedekind uses definitions contrary to WM's assertion.