Additive identity

In mathematics, the additive identity of a set that is equipped with the operation of addition is an element which, when added to any element x in the set, yields x. One of the most familiar additive identities is the number 0 from elementary mathematics, but additive identities occur in other mathematical structures where addition is defined, such as in groups and rings. Elementary examples

The additive identity familiar from elementary mathematics is zero, denoted 0. For example, *:5+0 = 5 = 0+5.
In the natural numbers \N (if 0 is included), the integers \Z, the rational numbers \Q, the real numbers \R, and the complex numbers \C, the additive identity is 0. This says that for a number n belonging to any of these sets, *:n+0 = n = 0+n.

Formal definition Let N be a group that is closed under the operation of addition, denoted +. An additive identity for N, denoted

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (1)

Related publications

Related people

Related units

Related concepts (27)

Related concepts

Related courses (3)

Related courses

Related lectures (3)

Related lectures

Additive manufacturing inks or resins and additive manufactured structures

Esther Amstad, Alvaro Lino Boris Charlet, Matteo Hirsch

The invention relates to additive manufacturing inks and resins; methods of using said inks and resins in additive manufacturing; and additive manufactured articles made using said inks and resins.

2022

Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do. A field is thus

Ring (mathematics)

In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist. In other words, a ring is a set equipped wit

Addition

Addition (usually signified by the plus symbol ) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers r

MATH-410: Riemann surfaces

This course is an introduction to the theory of Riemann surfaces. Riemann surfaces naturally appear is mathematics in many different ways: as a result of analytic continuation, as quotients of complex domains under discontinuous group actions, as algebraic curves.

MATH-311: Rings and modules

The students are going to solidify their knowledge of ring and module theory with a major emphasis on commutative algebra and a minor emphasis on homological algebra.

MATH-479: Linear algebraic groups

The aim of the course is to give an introduction to linear algebraic groups and to give an insight into a beautiful subject that combines algebraic geometry with group theory.