Identity
Pronunciation: /aɪˈdɛn.tɪ.ti/ Explain
An identity is a value and an
operation such that
applying
the value and operation does not change the result.
The
additive identity
for
real numbers
is 0. This is because one can add 0
to any value, and the result is the same. Example: 3 + 0 = 3.
The
multiplicative identity
for real numbers is 1. This is because one can multiply
1 by any value, and the result is the same. Example:
-5 · 1 = -5.
Identity | Description |
a + 0 = a | The
additive identity for real numbers
is the number 0. This is because, for any real number
a, a + 0 = a. |
a·1 = a |
The multiplicative identity for real
numbers is 1. You can see
that a·1 = a. |
| The identity for a square matrix
under multiplication is a diagonal matrix
where every diagonal value is
1. |
- An identity is an
equation
that is true for all values of the
variables
used in the equation. One example of an identity is the equation
sin(x)^{2}+cos(x)^{2} = 1. This identity
is always true for any value of x. An identity can be used to
solve
equations or find the derivative of equations by transforming an equation into
a more useful form:
Equation | Description |
sin(x)^{2}+sin(x) = 1-cos(x)^{2} | Equation to solve. |
sin(x)^{2}+cos(x)^{2}+sin(x) = 1 | Add cos(x)^{2} to both sides of the equations. |
1+sin(x) = 1 | Substitute 1 for sin(x)^{2}+cos(x)^{2}. |
sin(x) = 0 | Subtract 1 from both sides. |
x ∈ {0, π, 2π, 3π, ...} | Transform equation from trigonometric form to set form. |
Table 1: Using an identity to solve an equation. |
References
- McAdams, David E.. All Math Words Dictionary, identity. 2nd Classroom edition 20150108-4799968. pg 93-94. Life is a Story Problem LLC. January 8, 2015. Buy the book
- Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pg 17. www.archive.org. International Textbook Company. January 1963. Last Accessed 8/7/2018. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n18/mode/1up. Buy the book
- Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pp 29-30. Thomson, Brooks/Cole. 2005. Last Accessed 8/7/2018. Buy the book
- Mary Jane Sterling. Algebra II For Dummies. pg 12. For Dummies. June 19, 2006. Last Accessed 8/7/2018. Buy the book
More Information
- McAdams, David E.. Additive Identity. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2/11/2010. http://www.allmathwords.org/en/a/additiveidentity.html.
Cite this article as:
McAdams, David E. Identity. 3/17/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/i/identity.html.
Image Credits
Revision History
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
8/6/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (
McAdams, David E.)
2/11/2010: Added "References". (
McAdams, David E.)
8/9/2008: Added More Information, definition 2. (
McAdams, David E.)
7/12/2007: Initial version. (
McAdams, David E.)