I need to prove the following:
1.) The intersection (infinity on top, n=1 on bottom) of the open interval (0,1/n) = the null set
2.) the intersection (infinity on top, m=1 on bottom) of the interval [m, infinity) = the null set
How do you show these? Why don't they adhere to the Nested Interval Property?
Here again is another way.
In a previous reply I gave you this lemma.
If e>0 then is a positive integer K such that (1/K)<e.
Looking at the intersection of the collection of sets (0,1/n), if it were not empty then it would contain some e>0. But e is not in set (0,1/K) in the collection, hence a contradiction. The intersection must be empty.