Axiom:Axioms of Uncertainty/Axiom 3

Axiom
$H$ fulfils the following axiom:
 * $\map {H_n} {p_1, p_2, \ldots, p_n} \ge 0$

and:
 * $\map {H_n} {p_1, p_2, \ldots, p_n} = 0$ $\exists i \in \set {1, 2, \ldots, n}: p_i = 1$

That is, uncertainty is always a positive quantity, and only reaches zero when one of the arguments is $1$.