Help on lim sup and lim inf

  • Thread starter funcalys
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  • #1
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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=[itex]\frac{1}{n}[/itex], I can easily check that 0 is its limit point but I don't know how to find it.:frown:
 
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  • #2
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.
 
  • #3
Never mind, I grasped the idea at last :biggrin: , but thanks aw.
 
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