bijection

Definition

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

Etymology

PIE word *dwóh₁ From French bijection, introduced by Nicolas Bourbaki in their treatise Éléments de mathématique.

Example Sentences

• "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."

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