Suppose that P1, P2, P3, ..., Pn,... are a sequence of statement variables. Suppose also that pk Pk+1 for any positive integer k. Then P1 > Pr for any integer n larger then 1? Why? [Select] Note that if the truth of the statement P1(called the base case), and the truth that pk => Pk+1 for any positive integer k (called the inductive step) are established, then Pris proven true for any integer n, using P1 Pr and modus ponens. This method of proof is known as the principle of mathematical induction. Suppose that P1, P2, P3, ..., Pn,... are a sequence of statement variables. Suppose also that pk =Pk+1 for any positive integer k. Then P1 Pn for any integer n larger then 1? Why? [ Select ] [ Select ] Note that if the truth of the statement Pi (called the bas Specialization. Generalization. integer k (called the inductive step) are established, then Division into cases. . modus ponens. This method of proof is known as the pr Transitivity Pk+1 for any positive Irn, using Pi - pr and