Warm-Up Problem • • • • • • • Theorem: For any n≥0, n2 ≥ n Try a few cases to see if it makes sense Cardinality If n=0, 02≥0 If n=1, 12≥1 How Big is a Set? Proof by induction… Base case: n=0: 02≥0 ✔ Induction: Assume n≥0 and P(n), prove P(n+1) 1/18/12% Harry%Lewis/CS20/CSCI%E4120/with%thanks%to%Albert%R.%Meyer% 1% Warm-Up Problem • • • • Assume n2≥n Then n2+2n ≥ n n2+2n+1 ≥Cardinality n+1 (n+1)2 ≥ n+1 ✔ How Big is a Set? 1/18/12% Harry%Lewis/CS20/CSCI%E4120/with%thanks%to%Albert%R.%Meyer% 1%