Decision Problem
Definition. A decision problem asks a yes/no question about every input: given a finite binary string, does it have the property or not. A problem is completely described by its answers, one bit per input string.
Decision problems are the course's central objects. There are uncountably many of them but only countably many programs, so some problems no program solves (Lecture 2, Example 6); naming one is the work of Lecture 7.