Element (Set)

Pronunciation: /ˈɛl.ə.mənt/ Explain

Example 1:

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

Example 2:

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

An object is an element of a set if it belongs to that set.[3] If object a is an element of set A, write aA. If object x is not an element of set P, write xP. 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. McAdams, David E.. All Math Words Dictionary, element (set). 2nd Classroom edition 20150108-4799968. pg 68. Life is a Story Problem LLC. January 8, 2015. Buy the book
  2. element. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 7/9/2018. http://www.merriam-webster.com/dictionary/element. Buy the book
  3. Jech, Thomas. Set Theory. 3rd edition. Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, CSLI, Stanford University. Last Accessed 7/9/2018. http://plato.stanford.edu/entries/set-theory/. Buy the book
  4. Goldrei, D.C.. Classic Set Theory: For Guided Independent Study. pg 3. Chapman & Hall Mathematics. July 1, 1996. Last Accessed 7/9/2018. Buy the book
  5. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pp 1-10. Thomson, Brooks/Cole. 2005. Last Accessed 7/9/2018. Buy the book

More Information

  • McAdams, David E.. Set. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 12/15/2009. https://www.allmathwords.org/en/s/set.html.

Cite this article as:

McAdams, David E. Element (Set). 4/20/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/e/element.html.

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Revision History

4/20/2019: Updated expressions and equations to match new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
7/5/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
1/24/2010: Added "References". (McAdams, David E.)
7/13/2008: Reorganized content for readability. Added example 3 (McAdams, David E.)
6/7/2008: Corrected spelling. (McAdams, David E.)
3/31/2008: Added member. (McAdams, David E.)
3/24/2008: Change More Information and Cite to current standards. (McAdams, David E.)
8/4/2007: Initial version. (McAdams, David E.)

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