chapter  14
12 Pages

Functions

EXAMPLE 14.2: Let Z be the set of integers and g = {(x,2x)lx E Z}. Is g a function from Z to Z? Now g C Z x Z, and dom(g) = Z and the implication [(x, yi) E g A (x, 92) E g = yl = y2] holds because (x, yi) E g and (x, y2) E g imply yi = 2x and y2 = 2x, hence yi = 2x = 92, so the answer to the question is yes, g is a function from Z to Z.