The addition and multiplication on Z, Q, R, and C are associative.

Subtraction is not.

Suppose X is a set. Let f, g, h be maps X -> X. Then the composition of f and g, notation fog, is the map X -> X given by

f·g (x) = f(g(x))    for x X.

Composition is a binary associative operation:

(f·g)·h(x) = f·g(h(x)) = f(g(h(x))) = f(g·h(x)) = f·(g·h)(x)