>>124614681. They don't think there is a controversy. They believe the axiom of infinity is something that should be unquestionably accepted.
2. Even if they did believe there was a controversy, they would relegate it to some advanced set theory class. A quarter/semester is too little time for even an intro set theory class to talk about different axiomatizations. And nobody gives a shit anyways.
Speaking from experience at a large public university, intro to analysis had ~200-300 people split over 5-6 different lectures.
Meanwhile, even the intro set theory class at the same university had 1 lecture with < 30 people and was infrequently offered due to a lack of lecturers.
Take /sci/ for example. Pic related is a typical chart (from the chart thread), that everyone here likes to jerk themselves off to. This one is actually better since there's at least some set theory.
However, notice it's always basic set theory; as in, here is what the axioms are, and here are some theorems based on it.
There's no real discussion of different approaches to foundations.
(cont)