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