Nit, decision problems are one type of computable problems, but you have other types like function problems, optimization problems, etc. NP, by definition invo

Nit, decision problems are one type of computable problems, but you have other types like function problems, optimization problems, etc. NP, by definition involves decision problems, but many NP-Hard problems are optimization problems. More specifically NP is the set of decision problems solvable by a NTM in poly time with the following conditions: 1) If the answer is "yes," at least one computation path accepts. 2) If the answer is "no," all computation paths reject Equivalently is is the set of decision problems verifiable by a TM in poly time. Modern programming tends to only care about #1, and structured programming paradigm helps with that. People not moving past NP in complexity theory is the real problem here. I also blame using the 'trys all answers at once' NTM intuition vs the max lucky guesser which makes it less silly. But didactic half truths do really hurt. Entscheidungsproblem is better for teaching people in my experience.