bijection

Definitions

A one-to-one correspondence, a function which is both a surjection and an injection.

Equivalents

Examples

“The present⟳ text has defined a set⟳ to be finite if and only if there exists a bijection onto a natural number⟳, and infinite if and only if there does not exist⟳ any such bijection.”

“Note⟳ in particular that a function is a bijection if and only if it's both an injection and a surjection.”

“The basic idea is that two sets A and B have⟳ the same cardinality if there is a bijection from A to B. Since the domain and range of the bijection is not relevant here, we often refer⟳ to a bijection from A to B as a bijection between the sets, or a one-to-one correspondence between the elements of the sets.”

CEFR level