Understanding lim sup and lim inf: Finding limit points and subsequential limits

[funcalys]

Hi everyone,
I'm currently having problems with these concept, my textbook states that:
Let S be the set of all subsequential limits of s_n, then
sup S= limsup s_n
inf S= liminf s_n
Knowing that S is also the set of all limits point of s_n, however I'm wondering how I could determine this set.
Ex: For s_n=$\frac{1}{n}$, I can easily check that 0 is its limit point but I don't know how to find it.

 

[algebrat]

You say "easily check", and "I don't know how to find it". It's not clear to me where you are stuck. Are you wondering how to show S={0}? If so, how about showing each is a subset of the other?

Please let us know if your question lies somewhere else.

 

[funcalys]

Never mind, I grasped the idea at last , but thanks aw.