Limit of a Monotonic Set Sequence

Last updated Nov 1, 2022

Let $({A}{n}){n=1}^{\infty}$ be a Sequence of Sets. Then if $(A_{n})$ is Non-Decreasing Function $$\lim\limits_{n \to \infty} A_{n} = \bigcup\limits_{n \in \mathbb{N}} A_{n},$$ an if $(A_{n})$ is Non-Increasing Function then $$\lim\limits_{n \to \infty} A_{n} = \bigcap\limits_{n \in \mathbb{N}} A_{n}.$$