Definition:Limit of Decreasing Sequence of Sets

Definition
Let $\left({A_n}\right)_{n \in \N}$ be a decreasing sequence of sets.

Let $A = \displaystyle \bigcap_{n \in \N} A_n$.

Then $A$ is said to be the limit of $\left({A_n}\right)_{n \in \N}$, and one writes $A_n \downarrow A$.