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The standard explanation of integrals as summing the areas of rectangles of decreasing width seems extremely intuitive to me without requiring the baggage of having to know some computer language. Generating functions in code are basically a rote repetition of the mathematical definitions, requiring that you also understand variables and functions and other things unrelated to the core idea.

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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.

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