Nested Interval Property

Nested Interval Property - 폐구간 수렴 정리

# Definition of the Nested Interval Let $(I_{n})_{n\in \mathbb {N}}$ be a sequence of closed intervals of the type $I_{n}=\left[a_{n},b_{n}\right]$, where $\mid I_{n} \mid \colon = b_{n} - a_{n}$ denotes the length of such an interval. One can call $(I_{n})_{n\in \mathbb {N}}$ a sequence of nested intervals, if 1. $\quad \forall n\in \mathbb {N} :\;\;I_{n+1}\subseteq I_{n}$ 2. $\quad \forall \va..