mapping
or map, n. a function or transformation. The language of mappings is often preferred for functions between abstract spaces. For some authors, a mapping is an ordered pair made up of a function together with a given codomain (a prescribed set containing the range of the function) while a function remains a set of ordered pairs. In this sense, the mapping
f : I+ → R : n ∣→ 1/n
of the positive integers into the rationals, taking each to its reciprocal, is different from the mapping
f : I+ →]0, 1] : n ∣→ 1/n,
although both are the set of ordered pairs 〈n, 1/n〉. Where there is no qualification stated, there is generally no implication that the mapping is either injective or surjective; but in some non-technical usage a mapping is taken to be one-to-one unless stated to the contrary. Discrete mappings are often represented by diagrams such as that below
See also domain.
f : I+ → R : n ∣→ 1/n
of the positive integers into the rationals, taking each to its reciprocal, is different from the mapping
f : I+ →]0, 1] : n ∣→ 1/n,
although both are the set of ordered pairs 〈n, 1/n〉. Where there is no qualification stated, there is generally no implication that the mapping is either injective or surjective; but in some non-technical usage a mapping is taken to be one-to-one unless stated to the contrary. Discrete mappings are often represented by diagrams such as that below