(adsbygoogle = window.adsbygoogle || []).push({}); The Nested interval theorem:If A_{n}= [a_{n}, b_{n}] is a sequence of closed intervals such that A_{n+1}[itex]\subseteq[/itex] A_{n}for all n [itex]\in[/itex] N, then [itex]_{n \in n}\bigcap[/itex]A = ∅.

I think of the case where a1=a2=...=an and b1=b2=...=bn for all n, hence every set A(n+1) will be the "subset" of A(n) and the intersection is the original closed interval. So I think the theorem in my textbook have some problem. Any correction for this ?

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# Nested interval theorem

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