2.7: Cardinality

When we talk about the number of elements in a set, we use the word cardinality. You’d think we could just call it the “size" of the set, but mathematicians sometimes like words that sound cool. The cardinality of \(M\) (the set of males, where the Davies family is the domain of discourse) is 3, because there are three elements in it. The cardinality of the empty set \(\varnothing\) is 0. The cardinality of the set of all integers is \(\infty\). Simple as that.

The notation we use for cardinality is vertical bars, like with absolute value. So we write: \(|M| = 3\).

To restate the example immediately above, \(|\varnothing| = 0\), but \(|\{\varnothing\}| = 1\).

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