# Differences

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 set_limes_inferior [2013/06/22 17:20]nikolaj created set_limes_inferior [2014/10/25 19:13]nikolaj 2014/10/25 19:13 nikolaj 2014/10/25 19:13 nikolaj 2014/03/21 11:11 external edit2013/06/22 17:20 nikolaj created Next revision Previous revision 2014/10/25 19:13 nikolaj 2014/10/25 19:13 nikolaj 2014/03/21 11:11 external edit2013/06/22 17:20 nikolaj created Last revision Both sides next revision Line 1: Line 1: ===== 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 ==== Line 29: Line 26: 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]]