**Homework #2
Due Thursday, September 3
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**Consider the set where we define 1'=2, 2'=3, 3'=4,..., and also define***A*'=*B*and*B*'=*A*. We showed in class that*N*satisfies the first four Peano axioms. Prove that*N*does not satisfy the fifth axiom by finding a subset*M*of*N*that satisfies*I*and*II*but yet*M*does not equal*N*.**Induction problems 1 and 7 in section 2.7 of the notes.**

Wed Sep 2 14:35:14 EDT 1998