Observe that the sequence 12, 15, 8, 13, 7, 18, 19, 11,
Chapter 9, Problem 38E(choose chapter or problem)
Observe that the sequence 12, 15, 8, 13, 7, 18, 19, 11, 14, 10 has three increasing subsequences of length four: 12, 15, 18, 19; 12, 13, 18, 19; and 8, 13, 18, 19. It also has one decreasing subsequence of length four: 15, 13, 11,10. Show that in any sequence of n2 + 1 distinct real numbers, there must be a sequence of length n + 1 that is either strictly increasing or strictly decreasing.
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer