 Nonnegative real number

A nonnegative real number is a real number $x\ge 0$. The set of all such numbers is ${\mathbb{R}}_{\ge 0}=[0,\infty )$, which includes zero as well as the positive real numbers. The word nonnegative is therefore weaker than strictly positive.

This set is closed under addition and multiplication, but negating a nonzero member leaves it. Every real square and every absolute value is nonnegative. A variance can equal zero, as it does for a constant random variable; calling every variance positive would incorrectly exclude that legitimate case. Nonnegative constraints similarly allow zero as a feasible boundary value in mathematical optimization.