Additive Identity

Pronunciation: /ˈæd ɪ tɪv aɪˈdɛn tɪ ti/ ?

An additive identity is the value that, when added to any other values in a set, returns the other value.[1] For real numbers, the additive identity is 0. This is because for any real number a, a + 0 = a.

For complex numbers the additive identity is 0 + 0i which can also be written 0.

Examples

3 + 0 = 3
-4 + 0 = -4
p + 0 = p
-t + 0 = -t
(4 + 2i) + (0 + 0i) = (4 + 2i)

References

  1. additive identity. merriam-webster.com. Encyclopedia Britannica. (Accessed: 2009-12-24). http://www.merriam-webster.com/dictionary/additive identity.
  2. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry, pg 17. International Textbook Company, January 1963. (Accessed: 2010-01-12). http://www.archive.org/stream/algebraandtrigon033520mbp#page/n18/mode/1up.
  3. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra, 6th edition, pp 29-30. Thomson, Brooks/Cole, 2005.
  4. Mary Jane Sterling. Algebra II For Dummies, pg 12. For Dummies, June 19, 2006. (Accessed: 2010-02-11).

More Information

  • McAdams, David. Identity. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2010-02-11. http://www.allmathwords.org/article.aspx?lang=en&id=Identity.
  • McAdams, David. Additive Inverse. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Additive%20Inverse.

Printed Resources

Cite this article as:


Additive Identity. 2009-12-24. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/additiveidentity.html.

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Revision History


2009-12-24: Added "References" (McAdams, David.)
2009-02-18: Corrected math error (McAdams, David.)
2008-10-05: Expanded 'More Information' (McAdams, David.)
2008-06-16: Added additive identity for complex numbers (McAdams, David.)
2008-06-07: Corrected spelling errors (McAdams, David.)
2008-05-29: Fixed grammar error (McAdams, David.)
2008-04-17: Initial version (McAdams, David.)

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