Problem
ALG-B3-M09-P017 Strict Positivity
#17
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Let \(f\) be additive, \(f(x)>0\) for all \(x>0\), and \(f(1)=1\). Prove that \(f(x)=x\).
Strict positivity gives strict increasingness.
If \(x
Strict order as regularity.