# Definition:Zero

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## Disambiguation

This page lists articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended article.

**Zero** may refer to:

- Set Theory and Order Theory:
- The zero ordinal.
- The zero cardinal.

- Algebra:
- The zero of the numbers:
- 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. From this definition follow:
- The zero of the integers.
- The zero of the rational numbers.
- The zero of the real numbers.
- The zero of the complex numbers.

- The zero digit of the number base representation.

- The zero of the numbers:

- Abstract Algebra:
- The zero of the naturally ordered semigroup.
- A zero element of an algebraic structure $\struct {S, \circ}$: 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 $\struct {R, +, \times}$ such that $\forall a \in R: 0_R \times a = 0_R = a \times 0_R$.
- The zero of a field: that element $0_F$ of a field $\struct {F, +, \times}$ such that $\forall a \in F: 0_F \times a = 0_F = a \times 0_F$.
- Root of Polynomial
- Zero Mapping

- Analysis and Complex Analysis:
- A zero of a function: given a function $f$ (which will usually be either real-valued or complex-valued), an element $x$ such that $\map f x = 0$.