A function that is both an injection and a surjection. if
is a bijection, then for each
y in
Y there is a unique
x in
X with the property that
i.e. there is a one-to-one correspondence between the elements in
X and the elements in
Y. The sets
X and
Y will have the same number of elements, i.e. the same cardinality. There will be a unique function
such that
f and
f-1 are inverses to each other;
f-1 will also be a bijection.