Let A be a nonempty subset of R that is bounded above. Show that there is a sequence $\displaystyle (x_n) $ of elements of A that converges to sup A.

Can we say that since A is bounded above, so is ($\displaystyle x_n$), then ($\displaystyle x_n$) is nondecreasing since it's bounded above, and so $\displaystyle x=$ sup{$\displaystyle x_n; n \in N$} exist.