(a) Suppose that {an} is a convergent sequence of points all in [0, 1] (ie.

an∈[0, 1] for all n). Prove that limit of an as n-->∞ is also in [0, 1].

(b) Find a convergent sequence {an} of points all in (0, 1) such that limit of an as n-->∞

is not in (0, 1).