Interesting.

In Maths classes, we started with functions. Functions as list of pairs, functions defined by algebraic expressions, functions plotted on graph papers and after that limits. Sequences were peripherally treated, just so that limits made sense.

Simultaneously, in Physics classes we were being taught using infinitesimals, with the a call back that "you will see this done more formally in your maths classes, but for intuition, infinitesimals will do for now".