Originally Posted by particlejohn can you give me an example of where one's intersection is empty and another intersection is not? let $\displaystyle I = \left\{\frac{1}{n}\right\}$ take $\displaystyle L=1$ as its bound. so, $\displaystyle I \subseteq [-1,1]=[-1,0] \cup [0,1]$....
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You can see an example of Bolzano's theorem on: The prodigious memory of Van Bommel. Bolzano's theorem.
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