Despite having a math degree, somehow I never took an analysis class, so I can't common on that specifically (I do believe that's one of the places where analys

Despite having a math degree, somehow I never took an analysis class, so I can't common on that specifically (I do believe that's one of the places where analysis diverges from other field's conventions; that being said, I do believe it is fairly standard practice to specify whether naturals start from 0 or 1 in a paper). In naive set theory, starting with 1 poses some problems (specifically, you don't have numbers yet, so you start with the notion of the empty set, which you use to define 0, and then proceed from there). Starting the naturals from 0 is also problematic in group theory, since you lose the additive identity.