If x-n converges to x, then for any E > O, there is natural number N such that n ² № implies x_^ < x + ε. N 2. If (x_n) is a real sequence then it converges to a unique limit. 。. For any real sequence, lim (x_n)/(y_n) = lim (x_^) / lim (y_n). 4. If a sequence is not motonic but bounded then it is not convergent. 5. If a ≤x-n≤b for all n (so it is bounded) and is monitically increasing, then x-n ->x as D ->[infinity]-