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Real Analysis : Empty Set and Nested Interval Property

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Prove that: Intersection to infinity for n=1 (sign of intersection with infinity on top and n=1 in the bottom) of (0,1/n)=empty.
(Notice that this demonstrates that the interval in the Nested Interval Property must be closed for the conclusion of the theorm to hold.)

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A real analysis problem is solved.

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The nested sequence of open bounded intervals,

(0,1), (0,1/2), ...

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