Problem
COM-B2-M04-P005 A Common Point of Intervals
#5
★★☆☆☆ Level 2 of 5
Several intervals are given on a line. Any two of them have a common point. Prove that there is a point belonging to all intervals.
Choose the interval whose right endpoint is as far left as possible.
Let \([a,b]\) be an interval with the smallest right endpoint \(b\). Consider any other interval \([c,d]\). By the choice of \(b\), we have \(b\le d\).
Since \([a,b]\) and \([c,d]\) intersect, we cannot have \(b
A good example of choosing an extremal coordinate rather than a size.