Hi, I have a question about the following proposition:

Let S ⊂ R be a nonempty bounded set. Then there exists a monotone sequence {xn} such that xn ∈ S for each n ∈ N and limxn = inf (S).

How would one go about proving this? I know that a monotone sequence means that xn is greater or equal to xn+1 (or less than or equal to, but in this situation, because we want inf(S), we want monotone decreasing, right?).

Help?