You may have noticed that in our examples of injections , there are always at least as many elements in as there are in . Similarly, surjections always map to smaller sets, and bijections map to sets of the same size.
The cardinality of a set (written ) is the size of the set. However, for the time being, we will not use this definition by itself. Doing so will encourage you to write proofs about cardinality that don't apply to infinite sets.