Fact: Let a=lim sup an. Then for all ε>0, there exists N such that if n≥N, then an<a+ε ============================ 1) What is the "intuitive meaning" of this fact? I cannot seem to make sense of it... 2) Let a=lim sup an. Is it also true that: For all ε>0, there exists N such that if n≥N, then sup an<a+ε ? n≥N Why or why not? Thanks for explaining!