[the_af]

> why would we restrict it to natural numbers

We don't, that's the point. We abstract it above numbers, so that we can find that lists and natural numbers and many other things share the same "shape" when looked at from certain perspectives.

It's not about showing off, but about finding generalizations -- finding the "shape" of things -- that allow us to use the same abstractions over them.

And to talk about these shapes, we must use the appropriate vocabulary. It's shorter and more precise. Just like you say "function" instead of explaining what it means in lots of words every time you mean function.