Problem
ALG-B3-M01-P016 Surjective ladder
#16
★★★★★ Level 5 of 5
Find all surjective \(f:\mathbb N\to\mathbb N\) such that \(f(n+1)\ge f(n)+1\) for all \(n\in\mathbb N\).
Hint. Prove \(f(n)\ge n\), then use surjectivity.
Since \(f(1)\ge1\), induction gives \(f(n)\ge n\). If \(f(k)>k\) for some \(k\), then monotonicity would give \(f(n)>k\) for all \(n\ge k\), and for \(n
Goal: separate guessing the answer from a complete proof and domain check.