Problem
ALG-B3-M11-P015 Growth on Naturals
#15
★★★★★ Level 5 of 5
Let \(f:\mathbb N\to\mathbb N\), \(f(n)>n\), and \(f(f(n))=n+2\). Prove that \(f(n)=n+1\).
Let \(m=f(n)\).
We have \(m>n\) and \(f(m)=n+2\). But by the condition, \(f(m)>m\), so \(n+2>m\). Hence \(n
Order plus iteration.