Recent content by esahione

You're right. Thinking about it leads me to believe that the problem asked is equivalent to prove that if a sequence has a strictly monotonic subsequence, which would be f(f(f(n))), we have to show that the sequence itself is strictly monotonic. But this is not true.

But your example gives f(f(f(x)))=1/x, which isn't a polynomial. Here's what I think was Adriank's mistake: His function isn't f(f(f(x)))=x. His function is f(f(f(3n)))=3n, f(f(f(3n-1)))=3n-1 and f(f(f(3n-2)))=3n-2. While it is true that it is equivalent to f(f(f(x)))=x, it is not a...

I'll elaborate on this a little bit more. Suppose f(f(f(x))) is a strictly increasing polynomial function. This means that f(x) must be increasing, by the argument given above. Furthermore, since f(f(f(x))) is a polynomial, and since it is a composition of functions, f(x) must be a polynomial...

This seems quite trivial to me. If this is what you want to prove: Let f:N->N. If f(f(f(x))) is a strictly increasing polynomial, then f(x) is a strictly increasing polynomial as well. Proof: The constraint that f : N->N means that there can't be any negative number in the image. Therefore...

Well, I haven't done analysis yet. But I need not only to learn analysis, but to also to work on my foundations. The place I'm going to study at is IMPA (Brazilian Institute of Pure and Applied Mathematics). They expect me to know my math really, really well. That includes my statistics and...

Hello Everyone! I'm going to start a Graduate course in Mathematical Finance next year, and I need some brushing up on my mathematics. I've done the basics: Calculus and Linear Algebra. But where I'm going to, the least I'm going to need is to really know my Analysis. I'm an economics...