[agumonkey]

Math is done very very wrong, I don't think most teachers know enough math (sorry for that dubious and bold claim).

As a computer guy who hates state machines and was always obsessed with math, I feel that just about everything about maths is taught wrong from the get go.

Just the other day I learned about something inductive function got me curious about: linear ordering of structures as proof of termination. Turns out it's been studied in math for long: it's called a well-order. Fine.. thing is we're taught about linear recursion in HS .. but we have no pragmatic notion of induction except ~~ P n-1 => P n ~~ It's so cryptically compressed that I suspect no student beside aspies and other prodigies can have the slightest clue about that. Yet it's so important (and so obvious when shown).

[RBerenguel]

Induction is baked in the most “common” way of defining the naturals (Peano axioms). IIRC, it’s the definition I got for the “proper naturals” when I was in HS (but, my Maths teacher was a mathematician, and was who got me interested in them).