\begin{definition}[Definition:Limit Inferior of Sequence of Sets/Definition 1]
Let $\sequence {E_n : n \in \N}$ be a sequence of sets.
Then the '''limit inferior''' of $\sequence {E_n : n \in \N}$, denoted $\ds \liminf_{n \mathop \to \infty} E_n$, is defined as:
{{begin-eqn}}
{{eqn | l = \liminf_{n \mathop \to \infty} E_n
      | o = :=
      | r = \bigcup_{n \mathop = 0}^\infty \bigcap_{i \mathop = n}^\infty E_n
}}
{{eqn | r = \paren {E_0 \cap E_1 \cap E_2 \cap \ldots} \cup \paren {E_1 \cap E_2 \cap E_3 \cap \ldots} \cup \cdots
}}
{{end-eqn}}
\end{definition}