Problem
ALG-B3-M08-P003 Increasing Involution
#3
★★☆☆☆ Level 2 of 5
Let \(f:\mathbb R\to\mathbb R\) be strictly increasing and suppose \(f(f(x))=x\). Prove that \(f(x)=x\) for all \(x\).
Assume \(f(a)>a\) or \(f(a)
If \(f(a)>a\), increasingness gives \(f(f(a))>f(a)\), so \(a>f(a)\), contradiction. If \(f(a)
Key ordered-cycle template.