Real numbers/Nested intervals/Point/Fact/Proof/Exercise

Let ${}I_{n}$, ${}n\in \mathbb {N}$, be a sequence of nested intervals in ${}\mathbb {R}$. Prove that the intersection

$\bigcap _{n\in \mathbb {N} }I_{n}$

consists of exactly one point ${}x\in \mathbb {R}$.

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