/sci/ - Science & Math

>>12062081
It's a real nice book. The category theory presentation is a bit odd since it takes so long to define functors, but generally the first half of the book is just very easy going and clear.

>>12060854
Depends on what you mean by "the reals". The class of Dedekind reals have a relatively hard time being a set, if you like weak axiom systems, and then Dedekind and Cauchy don't really agree, even. There's also various interval definitions more restrictive than Cauchy's equivalence classes, or otherwise definitions that are presented jointly with the intended real number arithmetic (unlike defining a set of cardinality 2^N and then defining arithmetic over it).
There's also stream approaches to the reals that I find interesting.
But tbqh I can't say much if you don't break too far from the standard setting.

>>12060854
That's various interval definitions more restrictive than Cauchy's equivalence classes, or otherwise definitions that are presented jointly with the intended real number arithmetic (unlike defining a set of cardinality 2^N and then defining arithmetic over it)