Let us consider R , S , F . Suppose F is an isomorphism between R and S . Let given a , b . Let us consider R , S . There exists F which is an isomorphism between R and S .
R is an isomorphism between R and R .
R and R are isomorphic. If F is an isomorphism between R and S , then F -1 is an isomorphism between S and R . If R and S are isomorphic, then S and R are isomorphic. Suppose F is an isomorphism between R and S and G is an isomorphism between S and T . Then G F is an isomorphism between R and T .