bijectionn.

/bʌɪˈdʒɛkʃ(ə)n/

Etymology: < bi- comb. form after injection n. 5.

Mathematics.

A mapping that is both injective and surjective.

ΘΚΠ

the world > relative properties > number > arithmetic or algebraic operations > transformation > [noun] > correspondence > preserving relations or elements

inclusion1870

orthomorphosis1885

isomorphism1892

identity1910

homoeomorphism1918

homomorphism1935

topological mapping or transformation1939

isometry1941

Möbius transformation1941

injection map(ping)1950

monomorphism1954

bijection1963

surjection1964

1963 D. G. Bourgin Mod. Algebraic Topol. x. 215 If Ψ is both a monomorphism and an epimorphism, it is a bijection (so that a bijection is a sort of underprivileged bimorphism).

1968 E. T. Copson Metric Spaces vii. 86 A mapping f: E₁→E₂ which is both an injection and a surjection is called a bijection.

1975 I. Stewart Concepts Mod. Math. ix. 128 Quite generally, two sets will have the same number of elements if and only if there is a bijection between them.

1982 W. S. Hatcher Logical Found. Math. viii. 249 The theory of cardinals is the study of properties of sets that are invariant under bijections.

Derivatives

biˈjective adj. of the nature of or pertaining to a bijection.

ΘΚΠ

the world > relative properties > number > arithmetic or algebraic operations > transformation > [adjective] > having specific correspondence

orthogonal1852

permutational1888

isomorphic1892

birational1894

unary1931

homomorphic1935

symplectic1939

involutory1941

injective1952

monomorphic1958

bijective1962

surjective1964

1962 J. T. Moore Elem. Abstr. Algebra i. 8 A bijective mapping determines and is determined by a one-to-one correspondence between the elements of the two sets.

1982 W. S. Hatcher Logical Found. Math. iii. 82 It was Cantor (and also Dedekind) who defined the notion of cardinal similarity (i.e. sameness of number) of two sets as being the existence of a bijective (1-1 onto) correspondence between the two sets.

This entry has not yet been fully updated (first published 1993; most recently modified version published online June 2018).

单词	bijection
释义	bijectionn. /bʌɪˈdʒɛkʃ(ə)n/ Etymology: < bi- comb. form after injection n. 5. Mathematics. A mapping that is both injective and surjective. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > transformation > [noun] > correspondence > preserving relations or elements inclusion1870 orthomorphosis1885 isomorphism1892 identity1910 homoeomorphism1918 homomorphism1935 topological mapping or transformation1939 isometry1941 Möbius transformation1941 injection map(ping)1950 monomorphism1954 bijection1963 surjection1964 1963 D. G. Bourgin Mod. Algebraic Topol. x. 215 If Ψ is both a monomorphism and an epimorphism, it is a bijection (so that a bijection is a sort of underprivileged bimorphism). 1968 E. T. Copson Metric Spaces vii. 86 A mapping f: E₁→E₂ which is both an injection and a surjection is called a bijection. 1975 I. Stewart Concepts Mod. Math. ix. 128 Quite generally, two sets will have the same number of elements if and only if there is a bijection between them. 1982 W. S. Hatcher Logical Found. Math. viii. 249 The theory of cardinals is the study of properties of sets that are invariant under bijections. Derivatives biˈjective adj. of the nature of or pertaining to a bijection. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > transformation > [adjective] > having specific correspondence orthogonal1852 permutational1888 isomorphic1892 birational1894 unary1931 homomorphic1935 symplectic1939 involutory1941 injective1952 monomorphic1958 bijective1962 surjective1964 1962 J. T. Moore Elem. Abstr. Algebra i. 8 A bijective mapping determines and is determined by a one-to-one correspondence between the elements of the two sets. 1982 W. S. Hatcher Logical Found. Math. iii. 82 It was Cantor (and also Dedekind) who defined the notion of cardinal similarity (i.e. sameness of number) of two sets as being the existence of a bijective (1-1 onto) correspondence between the two sets. This entry has not yet been fully updated (first published 1993; most recently modified version published online June 2018). < n.1962
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