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.)
The nested sequence of open bounded intervals,
(0,1), (0,1/2), ...
A real analysis problem is solved.