Family of Closed/Open Nested Intervals

Question

Find a family $\{I_n\}$ of closed nested intervals, such that no two $I_n$'s are equal and their intersection is $[-2,2]$.

An answer for the same question except for dealing with open nested intervals would also be appreciated.

What if you made $[-2,2]$ slightly larger? – David Mitra Jan 25 '14 at 15:52 — David Mitra, Jan 25 '14 at 15:52

score 0 · Answer 1 · edited Jan 25 '14 at 16:19

0

How about...

$$ I_n=\left[-2-\frac{1}{n},2+\frac{1}{n}\right],\quad n \in \mathbb{N} $$

edited Jan 25 '14 at 16:19

answered Jan 25 '14 at 15:58

ireallydonknow

1 Answers1