Pointwise Operations and Characteristic Functions
Let U be a set, suppose f, g : U --> R are functions from U to the set of real numbers R, and Let a E R. Then f + g, fg. af: U --> R are defined by (f + g)(x) = f(x) + g(x), (fg)(x) = f(x)g(x) (af)(x) = a(f(x)) for all x E R. If a E R by abuse of notation we regard a as the constant function from U to R defined by a(x) =