*x_n indicates x sub n

*>= indicates greater than or equal to

Let (x_n) be a bounded sequence and for every n in natural numbers, let s_n:= sup {x_k : k>=n} and t_n:= inf {x_k : k>=n}

Prove that (s_n) and (t_n) are monotone and convergent. Also prove that if lim(s_n) = lim(t_n), then (x_n) is convergent.

Can someone get me started in the right direction? Thank you!