===== Set limes superior ===== ==== Set ==== | @#55CCEE: context | @#55CCEE: $A\in \text{Seq}(X)$ | | @#FF9944: definition | @#FF9944: $\underset{n\to\infty}{\limsup}A_n\equiv{\bigcup_{n=1}^\infty}\left({\bigcap_{k=n}^\infty}A_k\right)$ | ==== Ramifications ==== We have that $\underset{n\to\infty}{\limsup}A_n\subseteq \underset{n\to\infty}{\liminf}A_n,$ see [[Set limes inferior]]. If moreover $\underset{n\to\infty}{\limsup}A_n=\underset{n\to\infty}{\liminf}A_n,$ then we call it $\underset{n\to\infty}{\lim}A_n$ and say $A$ is //convergent//. === Reference === Wikipedia: [[http://en.wikipedia.org/wiki/Limit superior and limit inferior|Limit superior and limit inferior]] === Discussion === 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]] ==== Parents ==== Parameterized set === Parameter refinement of === [[Sequence union]] === Related === [[Sequence intersection]]