Paragraph

In general, \(\card{A} \ge \card{f(A)}\text{,}\) since you cannot get more outputs than you have inputs (each input goes to exactly one output), but you could have fewer outputs if the function is not injective. If the function is injective, then \(\card{A} = \card{f(A)}\text{,}\) although you can have equality even if \(f\) is not injective (it must be injective restricted to \(A\)).

in-context