What allows us to do calculus over ? I believe I've read the phrase 'complete, ordered field' with respect to it. I know completeness is necessary, and that there are other ways to complete the rationals to make calculus possible (p-adic numbers). I can see how the order and field properties are needed too. Must in this case also be a metric space in order to make definitions meaningful?

Basically, exactly what type of structure is when we do calculus over it?