Problem
ALG-B3-M11-P003 Involution with Order
#3
★★★★☆ Level 4 of 5
Let \(f:\mathbb R\to\mathbb R\) be strictly increasing and \(f(f(x))=x\). Prove that \(f(x)=x\).
Compare the cases \(f(a)>a\) and \(f(a)
If \(f(a)>a\), then \(f(f(a))>f(a)\), i.e. \(a>f(a)\), contradiction. The case \(f(a)
Iteration through order.