In article <email@example.com>, quasi <firstname.lastname@example.org> wrote:
> On Thu, 31 May 2007 23:07:58 -0500, quasi <email@example.com> wrote: > > I accidentally forgot to include "the rationals". > > Here's a corrected list ... > > > (3) Learn the standard axioms and definitions for > > > > the natural numbers > > the integers > the rationals > > the reals > > the complex numbers > > quasi
One can also proceed slightly differently, and some prefer to do it this way: The naturals The positive rationals The rationals (all of them) The reals The complexes
But in either case, when one proceeds from the rationals to the reals, the result is a complete Archimedean ordered field.
And in that field, if 0.999... is to have any meaning at all, it must mean the multiplicative identity of that field.