1.11.1 Cardinality Video
PROFESSOR: Cardinality is the word that's used to refer to the size of infinite sets. And before we go further, let's take a quick look at why we're interested in infinite sets in a course that's Mathematics for Computer Scientists. Why does computer science care about infinite sets? Well, like every data structure that you'd examine in computer memory is finite and the integers individually are finite, you only calculate with finite things. But, the infinite abstraction happens right at the beginning. Although any given integer is finite, the set of all integers is infinite. And although any given matrix is finite, the set of all the matrices that might be represented in a computation are an infinite set. So, we take infinite sets for granted and reason about them all the time. The second, from a pedagogical point of view, introducing the concept of infinite sets and reasoning about them carefully forces you to go beyond your intuition and really foll...