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Bijection, injection and surjection
In mathematics, injections, surjections and bijections are classes of functions distinguished by the manner in which arguments (input expressions from
Bijection
function (injection, not a bijection) An injective surjective function (bijection) A non-injective surjective function (surjection, not a bijection) A non-injective
Surjective function
necessarily a surjection. The composition of surjective functions is always surjective. Any function can be decomposed into a surjection and an injection. A surjective
Injective function
function (injection, not a bijection) An injective surjective function (bijection) A non-injective surjective function (surjection, not a bijection) A non-injective
Range of a function
inclusions being equality. Bijection, injection and surjection Hungerford 1974, page 3. Childs 1990, page 140. Dummit and Foote 2004, page 2. Rudin 1991
Domain of a function
{\displaystyle {\frac {\pi }{2}}+k\pi ,k=0,\pm 1,\pm 2,\ldots } . Bijection, injection and surjection Codomain Domain decomposition Attribute domain Effective
Map (mathematics)
function f and a list [v0, v1, ..., vn] as arguments and returns [f(v0), f(v1), ..., f(vn)] (where n ≥ 0). Bijection, injection and surjection – Properties
Outline of logic
relation Antisymmetric relation Asymmetric relation Bijection Bijection, injection and surjection Binary relation Composition of relations Congruence
Countable set
of {1, 2, 3}, and vice versa, this defines a bijection. We now generalize this situation and define two sets as of the same size if (and only if) there
S-box
bent function of the input bits is termed a perfect S-box. Bijection, injection and surjection Boolean function Nothing up my sleeve number Permutation