Let (xn) be a sequence of real numbers. Consider the set P = {n ∈ N ∶ xn > xm for all m ∈ N with m > n}. Then which of the following is/are true?
1
If P is finite, then (xn) has a monotonically increasing subsequence.
2
If P is finite, then no subsequence of (xn) is monotonically increasing.
3
If P is infinite, then (xn) has a monotonically decreasing subsequence.
4
If P is infinite, then no subsequence of (xn) is monotonically decreasing.