title: "Lecture 3 - Sets, Relations, and Functions"
unit: 0
lecture: 3

Lecture 3 - Sets, Relations, and Functions

(Skeleton for Fall 2026.)

Sets

TODO: notation, subsets, power sets, products; alphabets, strings, and languages as the sets we care about all semester.

Relations

TODO: equivalence relations and partitions (needed for Myhill-Nerode flavored arguments); orders.

Functions

TODO: injections, surjections, bijections; functions as the formal home of "problem" (language membership) and "resource bound" (f from N to N).