Let mathbb Z are isomorphic. {mathcal F}/cong and mathcal F by the relation of isomorphism. Prove that the sets U. Consider the equivalence ? defined on F be the set of finite subsets of mathbb Z, and let U be any set containing Solution Z is a subset of U. F is the set of finite subsets of U. F is a finite subset of U whereas Z is a infinite subset of U. Consider the finite subset of U contain n elements Then definite a mapping from Z to F such that Z -- Z mod n where n is the dimension of F Then it is seen that this is an isomorphism. Hence proved.