@Mathmuse Yes, technically you don't divide by zero in calculus, but it's pretty close to it. Practically speaking, finding the instantaneous rate of change is pretty close to "dividing by zero" in a defined way. To me, math was more like grammar lessons up until calculus where we actually got to flex our minds and create things out of infinitesimals and optimize things. In a sense, this was the fun part, and any time you deal with something in calculus you are always dealing with infinity in some form or another and I think it really made me love math when before that I didn't care much at all for it.
There's a very negative mindset towards math, so it seems foolish for anyone in here to be arguing against someone saying something enthusiastic about math such as, "You get to divide by zero" when really you're "Dividing by x as x approaches 0" as it's splitting hairs when most people here are saying "Math sucks" and seems to be should be encouraged to see how math can become something very interesting and philosophical.
Hell, e^ix=cosx+isinx is easily shown by comparing their representations as _infinite_ term polynomials. That's damn cool, if someone showed that to me in algebra 1 I would have been curious to find out how and might have made better grades in the past.