| 释义 |
bijection
bi·jec·tion B0244350 (bī-jĕk′shən)n. Mathematics A function that is both one-to-one and onto.
[bi- + (in)jection or (pro)jection.]bijection (baɪˈdʒɛkʃən) n (Mathematics) a mathematical function or mapping that is both an injection and a surjection and therefore has an inverse. See also injection5, surjectionTranslationsbijection
bijection[′bī‚jek·shən] (mathematics) A mapping ƒ from a set A onto a set B which is both an injection and a surjection; that is, for every element b of B there is a unique element a of A for which ƒ (a) = b. Also known as bijective mapping. bijection (mathematics)A function is bijective or a bijection or aone-to-one correspondence if it is both injective (no twovalues map to the same value) and surjective (for everyelement of the codomain there is some element of thedomain which maps to it). I.e. there is exactly one elementof the domain which maps to each element of the codomain.
For a general bijection f from the set A to the set B:
f'(f(a)) = a where a is in A and f(f'(b)) = b where b is in B.
A and B could be disjoint sets.
See also injection, surjection, isomorphism,permutation. |