I mean, ok, there's addition and then there's multiplication. Fine.
In addition 0 gives you the same and 1 gives you successor. In
mutliplication 0 gives you 0 and 1 gives you the same. Ok, we get it.
But that I could handle by referring to addition and multiplication intuition. But linear algebra, I got a C and had to convice my advisor to let me survive.
I get dot products but damn the rest of linear algebra and matrices were taught without any insight or intuition.
Anyway, kids: addition is a 10x10 ROM you're programmed with. Same for multiplication. Plus, in both instances, an algorithm for using that table
to handle arbitrary digit operations.
That is what elementary school "math" is: memorizing tables and
learning to perform algorithms.
