| Every x in X gets mapped to exactly one element in Y. | |
| For every x in X there is at most one y in Y such that f(x) = y. | |
| For every x in X there is at least one y in Y such that f(x) = y. | |
| For every y in Y there is some x in X such that f(x) = y. | |
| For every y in Y there is at most one x in X such that f(x) = y. | |
| For every y in Y there is exactly one x in X such that f(x) = y. | |
| f has an inverse f^{-1}. |