(thing) by hobyrne Wed Oct 10 2001 at 19:50:37

The codomain of a function f:A → B is {x : there is some a in A such that f(a) = x}, or, in Eindhoven notation, (∪ : a ∈ A : {f(a)}).

If the codomain of a function f:A → B is C, and B = C (i.e. if the range is equal to the codomain), then f is surjective. If B ≠ C, then there is a function g:A → C such that g(x) = f(x), and g is surjective.

Compare with domain and range.

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