Additive inverse

"Opposite number" redirects here. For other uses, see analog and counterpart.
For other uses, see Negation (disambiguation).

In mathematics, the additive inverse of an element x, denoted -x,[1] is the element that when added to x, yields the additive identity, 0.[2] In the most familiar cases, this is the number 0, but it can also refer to a more generalized zero element.

In elementary mathematics, the additive inverse is often referred to as the opposite number.[3][4] The concept is closely related to subtraction[5] and is important in solving algebraic equations.[6] Not all sets where addition is defined have an additive inverse, such as the natural numbers.[7]

  1. ^ Gallian, Joseph A. (2017). Contemporary abstract algebra (9th ed.). Boston, MA: Cengage Learning. p. 52. ISBN 978-1-305-65796-0.
  2. ^ Fraleigh, John B. (2014). A first course in abstract algebra (7th ed.). Harlow: Pearson. pp. 169–170. ISBN 978-1-292-02496-7.
  3. ^ Mazur, Izabela (March 26, 2021). "2.5 Properties of Real Numbers -- Introductory Algebra". Retrieved August 4, 2024.
  4. ^ "Standards::Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts". learninglab.si.edu. Retrieved 2024-08-04.
  5. ^ Brown, Christopher. "SI242: divisibility". www.usna.edu. Retrieved 2024-08-04.
  6. ^ "2.2.5: Properties of Equality with Decimals". K12 LibreTexts. 2020-07-21. Retrieved 2024-08-04.
  7. ^ Fraleigh, John B. (2014). A first course in abstract algebra (7th ed.). Harlow: Pearson. pp. 37–39. ISBN 978-1-292-02496-7.