A monotone sequence converges iff it is bounded. If I outline the proof, be able to give the reason for a statement or fill in a missing statement. Problems like assigned ones. Be able to determine if the sequence is bounded, mono. What a peak index is, be able to determine peak indices for a given sequence.
Every sequence has a monotone subsequence.
Know that every bounded sequence has a convergent subsequence, and how this follows from theorem 2.11 and the Montotone Convergence Theorem. The Bolzano-Weierstrass Theorem. Know the statement. Given a function, identify a maximum and minimum. Give a function whcih does not have a maximum or minimum.