Even if the world is fundamentally discrete, that does not mean that continuous models are not valuable. They are.

We are used to doing discrete approximations to continuous problems, but the other way around works too. For example, evaluating the sum

1 + 1/4 + ... + 1/n^2

is quite hard. On the other hand, we may approximate by the integral over x^2, which remarkably has an easy formula.

Continuous and discrete models complements each other, they are not mutually exlusive.