Definition:Zero


 * The zero ordinal.


 * The zero cardinal.


 * The zero of the natural numbers, a concept which follows from, and can be defined from, the definition of the natural numbers as the isomorphism class of a naturally ordered semigroup.


 * A zero element of an algebraic structure $\left({S, \circ}\right)$: an element $z \in S$ such that $\forall s \in S: z \circ s = z = s \circ z$.


 * The zero of a ring: that element $0_R$ of a ring $\left({R, +, \times}\right)$ such that $\forall a \in R: 0_R \times a = 0_R = a \times 0_R$.


 * A zero of a function: given a function $f$ (which will usually be either real-valued or complex-valued), an element $x$ such that $f \left({x}\right) = 0$.


 * A zero vector.


 * The empty category.