1) Prove that lim (Sn) = 0 iff lim|(Sn)| = 0.

Note: the || are absolute values.

2) Let (Sn) be a convergent sequence, and suppose that lim Sn > a.

Prove that htere exists a number N such that n > N implies Sn > a.

These are to be proved using the definition the limit of a sequence:

For each epsilon > 0 there exists a number N such that

n > N implies |Sn - L| < epsilon

Thank you so much I am very stuck right now.