/sci/ - Science & Math

>>12062305
you'd have to construct [math]\mathbb R[/math] through Dedekind cuts or some other wizardry which is often too boring for an undergraduate course. it's best to just mention it and if your department has a fundamentals course they can take that later
pic related constructs [math]\mathbb N[/math] from the Peano axioms in the first chapter, but then doesn't bother with building [math]\mathbb R[/math] the same way and just presents it in an axiomatic manner (i.e. "there exists a complete Archimedean ordered field" basically)

>>11614401
logic and real anal don't require calc at all.
>>11614370
my uni's math program was sort of like this — first semester "calc" was essentially an intro to logic and set theory (think the first bits of Transition to Advanced Mathematics), and then analysis on [math]\mathbb R[/math] (think pic related). I've heard some euro math programs are like this as well.