Equality of Sets

Pronunciation: /ɪˈkwɒlɪti ʌv sɛtz/ ?

Two sets are equal to each other if they contain exactly the same members[1]. Stated mathematically: A = B iff A ⊆ B and B ⊆ A. This means that if set A contains everything in set B and set B contains everything in set A, then the two sets have exactly the same contents and are equal.


  1. Jech, Thomas. Set Theory. Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, CSLI, Stanford University. (Accessed: 2009-12-15). http://plato.stanford.edu/entries/set-theory/.
  2. D.C. Goldrei. Classic Set Theory: For Guided Independent Study, pg 3. Chapman & Hall, July 1, 1996.
  3. Robert R. Stoll. Set Theory and Logic, pp 29-33. Dover Publications, October 1, 1979.
  4. Goldberg, Samuel. Probability: An Introduction, pg 5. Prentice Hall, 1960. (Accessed: 2010-01-25). http://www.archive.org/stream/probailityanintr000991mbp#page/n22/mode/1up/search/equal.

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.

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Cite this article as:

Equality of Sets. 2009-12-15. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/e/equal_set.html.


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Revision History

2010-01-25: Added "References" (McAdams, David.)
2008-07-15: Added more information (McAdams, David.)
2008-07-14: Expanded text (McAdams, David.)
2008-03-28: Initial version (McAdams, David.)

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