I'm trying to prove(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\bigcap^{\infty}_{n=1}(0,1/n) = [/tex] EMPTY SET.

One thing that I can't seem to bypass is getting past the closed intervals as stated in the Nested Interval Property, which states "For each [tex]n\in[/tex]N, assume we are given a closed interval [tex]I_n = [a_n, b_n] = {x \in[/tex]R[tex]: a_n \leq x \leq b_n}[/tex]. Assume also that each [tex]I_n[/tex] contains [tex]I_n_+_1[/tex].

Therefore, [tex]\bigcap^{\infty}_{n=1}I_n \neq [/tex] EMPTY SET.

Basically, I'm stuck at taking care of the open interval part of this proof. The original forRwas proved by showing sup A = x, then x is between the closed interval. Any advice would be great!

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# Proving an intersection empty set

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