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set_limes_inferior [2013/06/22 17:20]
nikolaj created
set_limes_inferior [2014/10/25 19:13] (current)
nikolaj
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 ===== Set limes inferior ===== ===== Set limes inferior =====
-==== Definition ​==== +==== Set ==== 
-| @#88DDEE: $A\in \text{Seq}(X)$ | +| @#55CCEE: context ​    | @#55CCEE: $A\in \text{Seq}(X)$ | 
- +| @#FF9944: definition ​ | @#FF9944: $\underset{n\to\infty}{\liminf}A_n\equiv{\bigcap_{n=1}^\infty}\left({\bigcup_{k=n}^\infty}A_n\right)$ | 
-| @#55EE55: $\underset{n\to\infty}{\liminf}A_n$ | +
- +
-| @#55EE55: ${\bigcap_{n=1}^\infty}\left({\bigcup_{k=n}^\infty}A_n\right)$ | +
  
 ==== Ramifications ==== ==== Ramifications ====
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 For a more possibly more elucidating explaination,​ see my answer in this Math.Se thread [[http://​math.stackexchange.com/​questions/​107931/​lim-sup-and-lim-inf-of-sequence-of-sets/​412395#​412395|this Math.SE thread]] For a more possibly more elucidating explaination,​ see my answer in this Math.Se thread [[http://​math.stackexchange.com/​questions/​107931/​lim-sup-and-lim-inf-of-sequence-of-sets/​412395#​412395|this Math.SE thread]]
  
-==== Context ​====+==== Parents ​====
 Parameterized set Parameterized set
  
 === Parameter refinement of === === Parameter refinement of ===
 [[Sequence intersection]] [[Sequence intersection]]
-=== Parents ​===+=== Related ​===
 [[Sequence union]] [[Sequence union]]
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