[Chris2048]

But that "standard explanation" is a process, not a definition. Riemann sums can't be used with all integrals.

In any case, if we stick with Riemann sums, there should be a strong relationship to Generating Functions (which there is).

> Generating functions in code are basically a rote repetition of the mathematical definitions

GFs with a mathematical basis may have, for example, set-theoretic definitions that are not similar to, say, Turing machines. Any non-constructivist math is automatically not like code.