Additive Identity

Pronunciation: /ˈæd.ɪ.tɪv aɪˈdɛn.tɪ.ti/ Explain

The additive identity of a number is the value that, when added to the number, returns that number.^[3] 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. McAdams, David E.. All Math Words Dictionary, additive identity. 2nd Classroom edition 20150108-4799968. pg 11. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. additive identity. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 6/12/2018. http://www.merriam-webster.com/dictionary/additive identity. Buy the book
3. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pg 17. www.archive.org. International Textbook Company. January 1963. Last Accessed 6/12/2018. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n18/mode/1up. Buy the book
4. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pp 29-30. Thomson, Brooks/Cole. 2005. Last Accessed 6/12/2018. Buy the book
5. Mary Jane Sterling. Algebra II For Dummies. pg 12. For Dummies. June 19, 2006. Last Accessed 6/12/2018. Buy the book

More Information

• McAdams, David E.. Identity. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/19/2018. https://www.allmathwords.org/en/i/identity.html.

Cite this article as:

McAdams, David E. Additive Identity. 4/9/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/a/additiveidentity.html.

Revision History

4/9/2019: Updated formatting of math objects. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
6/18/2018: Clarified wording. (McAdams, David E.)
6/12/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
12/24/2009: Added "References". (McAdams, David E.)
2/18/2009: Corrected math error. (McAdams, David E.)
10/5/2008: Expanded 'More Information'. (McAdams, David E.)
6/16/2008: Added additive identity for complex numbers. (McAdams, David E.)
6/7/2008: Corrected spelling errors. (McAdams, David E.)
5/29/2008: Fixed grammar error. (McAdams, David E.)
4/17/2008: Initial version. (McAdams, David E.)