Bijection

Quick meaning: Bijection is a noun meaning (set theory) A one-to-one correspondence, a function which is both a surjection and an injection.

Meaning

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

Example Sentences

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

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.

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.

Word Forms

• bijections

Related Words

Related dictionary entries include injection, injectivity, isomorphism, correspondence, surjectivity, semiconjugacy.

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