injection
1. A function, f : A -> B, is injective or one-one, or is an injection, if and only if for all a,b in A, f(a) = f(b) => a = b. I.e. no two different inputs give the same output (contrast many-to-one). This is sometimes called an embedding. Only injective functions have left inverses f' where f' (f(x)) = x, since if f were not an injection, there would be elements of B for which the value of f' was not unique. If an injective function is also a surjection then is it a bijection. 2. An injection function is one which takes objects of type T and returns objects of type C(T) where C is some type constructor. An example is f x = (x, 0). The opposite of an injection function is a projection function which extracts a component of a constructed object, e.g. fst (x,y) = x. We say that f injects its argument into the data type and fst projects it out. (1995-03-14) In addition suitable contents:
[ 2 ] [ = ] [ al ] [ am ] [ an ] [ ar ] [ arc ] [ arg ] [ argument ] [ as ] [ at ] [ av ] [ B ] [ b ] [ be ] [ bi ] [ bijection ] [ bj ] [ C ] [ ca ] [ ch ] [ co ] [ com ] [ component ] [ con ] [ cons ] [ constructor ] [ data ] [ data type ] [ dd ] [ diff ] [ ding ] [ du ] [ ec ] [ ed ] [ edu ] [ element ] [ embedding ] [ er ] [ es ] [ et ] [ fi ] [ file ] [ fo ] [ for ] [ function ] [ gi ] [ gu ] [ h ] [ hat ] [ hr ] [ id ] [ iff ] [ il ] [ in ] [ inc ] [ input ] [ int ] [ inverse ] [ io ] [ iq ] [ is ] [ it ] [ ke ] [ ld ] [ Lex ] [ ls ] [ lu ] [ ly ] [ ma ] [ man ] [ mo ] [ mod ] [ module ] [ mp ] [ na ] [ nc ] [ ne ] [ ng ] [ ni ] [ nl ] [ no ] [ np ] [ ns ] [ O ] [ object ] [ om ] [ op ] [ output ] [ pe ] [ ph ] [ pl ] [ pr ] [ projection ] [ query ] [ rc ] [ re ] [ reduction ] [ ro ] [ ru ] [ sa ] [ sam ] [ say ] [ se ] [ si ] [ sit ] [ so ] [ st ] [ struct ] [ su ] [ surjection ] [ T ] [ th ] [ to ] [ tp ] [ tr ] [ tw ] [ type ] [ um ] [ va ] [ value ] [ ve ]
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