Element (Set)

Pronunciation: /ˈɛlə mənt/ ?

Example 1:

Disc representing set A with elements a, b, and c.
Figure 1: a ∈ A

Example 2:

Disc representing set P with elements p, q, and r, and x outside the disc.
Figure 2: x ∉ P

An object is an element of a set if it belongs to that set.[1] If object a is an element of set A, write a ∈ A. If object x is not an element of set P, write x ∉ P.

A member of a set is the same thing as the element of a set.

Example 3

Let S be the set of all integers. Then:
  • 1 ∈ S since 1 is an integer;
  • 1.5 ∉ S since 1.5 is not an integer.


  1. element. merriam-webster.com. Encyclopedia Britannica. (Accessed: 2010-01-24). http://www.merriam-webster.com/dictionary/element.
  2. Jech, Thomas. Set Theory. Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, CSLI, Stanford University. (Accessed: 2010-01-24). http://plato.stanford.edu/entries/set-theory/.
  3. D.C. Goldrei. Classic Set Theory: For Guided Independent Study, pg 3. Chapman & Hall, July 1, 1996. (Accessed: 2010-01-24).
  4. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra, 6th edition, pp 1-10. Thomson, Brooks/Cole, 2005.

More Information

  • McAdams, David. Set. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-12-15. http://www.allmathwords.org/article.aspx?lang=en&id=Set.

Printed Resources

Cite this article as:

Element (Set). 2010-01-24. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/e/element.html.


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Revision History

2010-01-24: Added "References" (McAdams, David.)
2008-07-13: Reorganized content for readability. Added example 3 (McAdams, David.)
2008-06-07: Corrected spelling (McAdams, David.)
2008-03-31: Added member (McAdams, David.)
2008-03-24: Change More Information and Cite to current standards (McAdams, David.)
2007-08-04: Initial version (McAdams, David.)

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