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A function <math>f : X \to \R</math> is called ''{{em|{{visible anchor|positive}}}}''{{sfn|Narici|Beckenstein|2011|pp=120-121}} or ''{{em|{{visible anchor|nonnegative}}}}'' if <math>f(x) \geq 0</math> for all <math>x \in X.</math>
It is called ''{{em|{{visible anchor|symmetric}}}}'' if <math>f(-x) = f(x)</math> for all <math>x \in X.</math>
Every subadditive symmetric function is necessarily nonnegative.
A sublinear function on a real vector space is symmetric if and only if it is a [[seminorm]].
The set of all sublinear functions on <math>X,</math> denoted by <math>X^{\#},</math> can be [[Partial order|partially ordered]] by declaring <math>p \leq q</math> if and only if <math>p(x) \leq q(x)</math> for all <math>x \in X.</math>
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