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