Consider the set [itex] A_n=\{0.9, 0.99, 0.999,...\} [/itex], where the greatest element of [itex] A_n [/itex] has [itex] n [/itex] 9s in its decimal expansion. Then [itex]0.999\ldots=1\in\bigcap_{n=1}^\infty{A_n}[/itex]. Is this possible even though [itex]\not\exists{n}(1\in{A_n})[/itex]?(adsbygoogle = window.adsbygoogle || []).push({});

Edit: I see that [itex]0.999\ldots=1\not\in\bigcap_{n=1}^\infty{A_n}[/itex]. Sorry :(.

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# Infinite intersection of indexed sets

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