Extend? Yes. Math is a tool that came from a context, so there might be implicit assumptions made on choosing that particular notation and definition that might or might not be justified. Appreciating where and idea comes from lets you work with the idea. I also think it helps learning and generalising.
A competent programmer with no knowledge of history can deal with things like e.g. non-monotonicity in time by just writing robust code. But it helps to know where it comes from: clock drift, user modification, error, leap seconds etc. If you know one of these, you can leverage different assumptions.
Extend? Yes. Math is a tool that came from a context, so there might be implicit assumptions made on choosing that particular notation and definition that might or might not be justified. Appreciating where and idea comes from lets you work with the idea. I also think it helps learning and generalising.
A competent programmer with no knowledge of history can deal with things like e.g. non-monotonicity in time by just writing robust code. But it helps to know where it comes from: clock drift, user modification, error, leap seconds etc. If you know one of these, you can leverage different assumptions.