Go backward to Function Inversion Go up to Top Go forward to Commutative Diagrams

Function Composition

Proposition: The composition of two functions is also a function,.

forall f, g, A, B, C:

f: A -> B /\  g: B -> C =>

f o g: A -> C.

Proof: see lecture notes (will be discussed later).

Proposition: direct characterization of function composition

forall f, g, A, B, C:

f: A -> B /\  g: B -> C =>

forall x in A: (f o g)(x) = g(f(x)).