Identity

Pronunciation: /aɪˈdɛntɪti/ ?
  1. 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.

    IdentityDescription
    a + 0 = aThe additive identity for real numbers is the number 0. This is because, for any real number a, a + 0 = a.
    1 = aThe multiplicative identity for real numbers is 1. You can see that a·1 = a.
    3 x 3 identity matrixThe identity for a square matrix under multiplication is a diagonal matrix where every diagonal value is 1.
  2. 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:
    EquationDescription
    sin(x)2+sin(x) = 1-cos(x)2Equation to solve.
    sin(x)2+cos(x)2+sin(x) = 1Add cos(x)2 to both sides of the equations.
    1+sin(x) = 1Substitute 1 for sin(x)2+cos(x)2.
    sin(x) = 0Subtract 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

  1. identity. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=identity&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
  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. Additive 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=Additive Identity.
  • McAdams, David. Multiplicative 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=Multiplicative Identity.
  • McAdams, David. Trigonometric Identities. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2010-02-11. http://www.allmathwords.org/article.aspx?lang=en&id=Trigonometric Identities.

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Identity. 2010-02-11. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/i/identity.html.

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2010-02-11: Added "References" (McAdams, David.)
2008-08-09: Added More Information, definition 2 (McAdams, David.)
2007-07-12: Initial version (McAdams, David.)

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