Problem
ALG-B1-M08-P018 Nonnegativity instead of monotonicity
#18
★★★★☆ Level 4 of 5
Let \(f:\mathbb R\to\mathbb R\) be additive and suppose \(f(t)\ge0\) for all \(t\ge0\). Prove that \(f(x)=cx\) for some \(c\ge0\).
First show that \(f\) is nondecreasing.
If \(x
Shows how a sign condition turns into monotonicity.