Define the function f:(0,1)→(0,1) by f(x)={x+21x2ifx<21ifx≥21 Let a and b be two real numbers such that 0<a<b<1. We define the sequences an and bn by a0=a,b0=b, and an=f(an−1), bn=f(bn−1) for n>0. Show that there exists a positive integer n such that (an−an−1)(bn−bn−1)<0.Proposed by Denmark