In my first A-to-Z I wrote a good number of pieces about the kinds of functions there are. For example, jump, a particular kind of discontinuity in functions. This is useful because there are a lot of pieces of functional analysis where we know things are true for continuous functions. And if a function has a jump discontinuity? Usually we know the thing is true except at the discontinuity. There’s more rules, of course. And, like, Fourier series will get strange around jump discontinuities.
I’d have written the essay a bit different today, but I am in awe of a time I could wrap up the point within six hundred words. That never happens anymore.