chapter  29
10 Pages

Axiom of Choice

Introduction: Suppose {a, b, c}, In, el and {y} are subsets of the alphabet and S

is the set {{a, b, c}, {n, e}, {y}, Q} of nonempty sets. Is there a set H consisting of exactly one element from each member of S? In this case the answer seems obvious. Since each T E S is nonempty, an element may be selected from it. Then the set H is formed from the selected elements. For example, a possible H would be H = {a, n, y, 0.5}.