Suppose f is a function or operation that acts on things we shall denote generically by the lower-case Roman letters x and y. Suppose it makes sense to multiply x and y by numbers (which we denote by a), and that it makes sense to add things like x and y together. We say that f is linear if for every number a and every value of x and y for which f(x) and f(y) are defined, (i) f( a×x ) is defined and equals a×f(x), and (ii) f( x + y ) is defined and equals f(x) + f(y). See affine.