[math-fun] I dream in math now.

So apparently I dream math problems now. Let f(n) be the smallest number such that what ever order you arrange the numbers from 1 to f(n) in, there is either an increasing subsequence or a decreasing subsequence of length n. What is f(n)? (JB, it seems unlikely that you care about this in real life, but in my dream, it was very important to you, for some practical application, to know that f(n) < n^2. You couldn't prove it though, and I said I would help.) f(1) = 1 f(2) = 2 f(3) = 4 Andy