Let (x_n) be a convergent sequence, and let a,b R.

Show that for all n, x_n>a ned not imply limx_n>a.

How do I show this when I have previously proven that If x_n>= a for all n, then lim x_n>=a. (this was another question that i had proven before hand) But how would I show it, when it contradicts the previously stated question.