let {$\displaystyle a_n$} $\displaystyle n \in N$ be a sequence of real numbers and suppose that lim $\displaystyle a_n = A$ as n goes to infinity, where A > 0. Prove that there exists $\displaystyle N_o \in N $ such that $\displaystyle a_n > 0$ for all $\displaystyle n > N_o$