Basis step: For we have only one object ( ) and only one permutation: i.e. we have permutations.
Induction step: Suppose that for objects we have permutations then ...
Hi. I have this practice problem (not-graded) in a chapter concerning inductive proofs:
I believe I understand the four steps of mathematical induction and can solve this, but I'm having trouble getting started: i.e., formulating the equation to be proved. Could someone point me in the right direction?Prove that for any natural number n, there are exactly n! permutations of n objects.