For nonempty sets \(A, B\) we say \[\begin{aligned} |A| \leq |B| &\text{ means there is a one-to-one function with domain $A$, codomain $B$} \\ |A| \geq |B| &\text{ means there is an onto function with domain $A$, codomain $B$} \\ |A| = |B| &\text{ means there is a bijection with domain $A$, codomain $B$} \end{aligned}\] For all sets \(A\), we say \(|A| = |\emptyset|\), \(|\emptyset| = |A|\) if and only if \(A = \emptyset\).