Definition:Zero


 * 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.


 * The zero 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.