6. Suppose that x and y are extended real numbers and {xn }, {Yn}, and {wn }

are real sequences.

(a) If Xn --+ x and Yn --+ x, as n --+ 00, and Xn ::; Wn ::; Yn for n E N, prove that Wn --+ x as n --+ 00.

(b) If Xn --+ x and Yn --+ y, as n --+ 00, and Xn ::; Yn for n E N, prove that x ::; y.