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 :(.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Infinite intersection of indexed sets

**Physics Forums | Science Articles, Homework Help, Discussion**