===== Set limes inferior =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $A\in \text{Seq}(X)$ |
| @#FF9944: definition  | @#FF9944: $\underset{n\to\infty}{\liminf}A_n\equiv{\bigcap_{n=1}^\infty}\left({\bigcup_{k=n}^\infty}A_n\right)$ | 

==== Ramifications ====
We have that

$\underset{n\to\infty}{\limsup}A_n\subseteq \underset{n\to\infty}{\liminf}A_n,$

see [[set limes superior]]. 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 intersection]]
=== Related ===
[[Sequence union]]