> the possible number of such relationships are infinite
I think you need to be careful taking about "infinite" in the context of math. If the number of quantities, relationships etc is finite, so are all their combinations. Even things like the infinit-ude of available numbers might have fixed patterns that render their relevant properties effecively finite, and lead to further distinctions e.g finite vs countable, etc.
Personally, I feel like math has a bit of a legacy problem. It holds on to the conventions of an art that is very old, with very different initial assumptions at its conception, and this is now holding it back somehow.
I lack the background to effectivly demonstrate this other than "Things I know/understand seem less intutive in standard mathenatical terms" e.g. generating functions and/or integrals feel easier to understand (to me) when you understand the, to be software-like 'loops'.
In fact, the idea of "constructivist math" seems (again, to me) to beg for a more algorithmic/computational approach.
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.
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.
I think you need to be careful taking about "infinite" in the context of math. If the number of quantities, relationships etc is finite, so are all their combinations. Even things like the infinit-ude of available numbers might have fixed patterns that render their relevant properties effecively finite, and lead to further distinctions e.g finite vs countable, etc.
Personally, I feel like math has a bit of a legacy problem. It holds on to the conventions of an art that is very old, with very different initial assumptions at its conception, and this is now holding it back somehow. I lack the background to effectivly demonstrate this other than "Things I know/understand seem less intutive in standard mathenatical terms" e.g. generating functions and/or integrals feel easier to understand (to me) when you understand the, to be software-like 'loops'.
In fact, the idea of "constructivist math" seems (again, to me) to beg for a more algorithmic/computational approach.