Mathematical induction can be used not only to prove equalities, but also to prove inequalities. The predicate P(n) is the statement n!

Extracted text: Mathematical induction can be used not only to prove equalities, but also to prove inequalities. The predicate P(n) is the statement n! < n"="" where="" n="" is="" an="" integer="" greater="" than="" 1.="" a)="" what="" is="" the="" statement="" p(2)?="" b)="" show="" that="" p(2)="" is="" true,="" i.e.,="" complete="" the="" basis="" step="" of="" the="" proof="" by="" induction.="" c)="" what="" is="" the="" inductive="" hypothesis="" of="" a="" proof="" by="" mathematical="" induction="" that="" p(n)="" is="" true="" for="" all="" natural="" numbers="" n="" greater="" than="" 1?="" recall="" that="" n!="" is="" the="" factorial="" of="" n,="" i.e.,="" n!="1·" 2.="" 3...="" 'n="" –="" 1)="" ·="">