Possible Duplicate:
Limit Supremum and Infimum. Struggling the concept
Hey I'm trying to figure out what $\limsup{S_{n}}$ is compared to $\lim{S_{n}}$ as well as the difference of $\lim{S_{n}}$ and $\liminf{S_{n}}$
So for example (this is my current thinking process) if I have a monotone non increasing sequence $S_{n}:=1/n$ (where $n=1$ and goes to infinity). The $\limsup{S_{n}}$ is 1, and $\liminf{S_{n}}$ is 0. But we know the $\lim{S_{n}}$ is 0.
How does $\lim{S_{n}}=\liminf{S_{n}}=\limsup{S_{n}}?$