How would you define the limit (if it exists) of a sequence of sets? What should the limit be if

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Step 1: Define the limit of a sequence of sets. The limit of a sequence of sets u005C( E_n u005C) as u005C(

How would you define the limit (if it exists) of a sequence of sets? What should the limit be if $E_1 \supset E_2 \supset \cdots$ ? If $E_1 \subset E_2 \subset \cdots$ ? Compute $\liminf _{n \rightarrow \infty} E_n$ and $\lim \sup _{n \rightarrow \infty} E_n$ in both cases and test your conjecture.