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set_limes_superior [2013/08/04 20:16] nikolaj |
set_limes_superior [2014/10/25 19:06] nikolaj |
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| ===== Set limes superior ===== | ===== Set limes superior ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $A\in \text{Seq}(X)$ | | + | | @#55CCEE: context | @#55CCEE: $A\in \text{Seq}(X)$ | |
| - | | @#55EE55: $\underset{n\to\infty}{\limsup}A_n$ | | + | | @#55EE55: postulate | @#55EE55: $\underset{n\to\infty}{\limsup}A_n$ | |
| - | | @#55EE55: ${\bigcup_{n=1}^\infty}\left({\bigcap_{k=n}^\infty}A_n\right)$ | | + | | @#55EE55: postulate | @#55EE55: ${\bigcup_{n=1}^\infty}\left({\bigcap_{k=n}^\infty}A_k\right)$ | |
| ==== 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 union]] | [[Sequence union]] | ||
| - | === Parents === | + | === Related === |
| [[Sequence intersection]] | [[Sequence intersection]] | ||
