I guess I've fallen through some of the cracks in the plethora of definitions I've learned, or I just never had enough examples of taking limits of intervals. Anyways, which is true, and why?(adsbygoogle = window.adsbygoogle || []).push({});

[tex]$\cap^{\infty}_{n=1}(0,\frac{1}{2^{n-1}}]=0?$[/tex]

[tex]$\cap^{\infty}_{n=1}(0,\frac{1}{2^{n-1}}]=\varnothing?$[/tex]

I think the first.

However, if I were to write the following instead:

[tex]$\lim _{n \rightarrow \infty} \cap_{n}(0,\frac{1}{2^{n-1}}]=\varnothing$[/tex],

would I be correct?

If not, why?

Thanks.

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# Examples of taking limits of intervals

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