In article <200603281814.k2SIEPl132120@walkabout.empros.com>, Michael Stemper <mstemper@siemens-emis.com> wrote:
> >So I hope that algebra book did not start out: A group is a set with a > >binary operation satisfying these axioms... > > <g> No, it started out with a few examples of groups and abstracted the > properties from them. *Then* it gave the formal definition.
And you can find topology texts that start out with examples of topologies and abstract the properties (arbitrary unions but only finite intersections) from them.
I wonder if Herman Rubin is reading this...He always says that the best technique for instruction is to begin with the abstract, then specialize...
