> If he had even said "a function is like a machine that takes number(s) as input, changes them with a formula and outputs the new number(s)", I think it would

> If he had even said "a function is like a machine that takes number(s) as input, changes them with a formula and outputs the new number(s)", I think it would have helped us grok. Helpful but not quite right and one of the common misconceptions students seem to carry over from high school. A function is something that takes inputs out of a set (its domain, e.g. people in this class) and gives you exactly one output with a prescribed data type (e.g. a date. The function than for instance being person -> birthdate). Neither numbers nor a formula are needed. > I think he understood math(s) so well that he couldn't relate to someone who didn't know what a function was. I think he probably could, but the syllabus said explicitly not discuss this ("too abstract") and there is time pressure. High school maths mostly is somewhat handwavy and stringing "definitions" together by examples. So you would mostly see lots of examples of functions and the "definition" of 'function' is then simply "things like that".