Good Math

Introducing the Transfinite Cardinals

Cardinality is a measure of the size of a set. For finite sets, that’s a remarkably easy concept: count up the number of elements in the set, and that’s its cardinality. When Cantor was first looking at the ideas of numbers and set theory, the first notion of the meaning of numbers that became clear was cardinality. If we have a set, one of the most obvious questions we can ask about it is “How big is it?” The measure of the size of a set is the number of elements in that set, which we call the set’s cardinality.

Once we have a notion of the size of a set, we can start asking questions about the relative size of sets: “Which set is bigger—this one or that one?” That question becomes even more interesting ...