Problem
ALG-B3-M08-P014 Minimal Growth
#14
★★★★★ Level 5 of 5
Let \(f:\mathbb N\to\mathbb N\), \(f(n)>n\) for all \(n\), and \(f(f(n))=n+2\). Prove that \(f(n)=n+1\).
Put \(m=f(n)\) and compare \(m\) with \(n+2\).
Let \(m=f(n)\). Then \(m>n\), and \(f(m)=n+2\). Applying the condition to \(m\), we get \(f(m)>m\). Hence \(n+2>m\). Thus \(n
Neat task on a chain and order in \(\mathbb N\).