@typhlosion I want this to exist and also I don't?

I'm bumping into students who are annoyed that their teacher told them x•x=x² ("there are two x's, so put a little ² over the x") but for some reason when they do the same thing and write x+x=x² their teacher takes off a bunch of points??

so there has to be some grounding the operations in a physical reality (or axioms) less arbitrary than "bishops/multiplication move diagonally and rooks/addition move orthogonally because that's what the rulebook says"

but there definitely seems to be something in this space that would be extremely helpful

@octopus @typhlosion I never understood why order of operations isn't just the order they're in

@MPurpureus order of operations *is* pure convention; this way just happens to need fewer parentheses most of the time

ax² + bx + c vs. a * (x²) + (b * x) + c

but sometimes you see

(+ (* a (^ x 2)) (+ (* b x) c))

as well

@MPurpureus having them go strictly in order messes with commutativity laws

going strictly in order
2 + 3 × 5 = 60
3 + 2 × 5 = 60
2 + 5 × 3 = 21

2 × 3 + 5 = 11
3 × 2 + 5 = 11
2 × 5 + 3 = 13

if we "clump" multiplication harder than addition, though
2 + 3×5 = 17
3×5 + 2 = 17 (we can swap clumps across a +)
2 + 5×3 = 17 (we can swap numbers across ×)

2×3 + 5 = 11
5 + 2×3 = 11
3×2 + 5 = 11

ack that should be = 25 for the first two, not 60