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.
References
- 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/.
- D.C. Goldrei. Classic Set Theory: For Guided Independent Study, pg 3. Chapman & Hall, July 1, 1996.
- Robert R. Stoll. Set Theory and Logic, pp 29-33. Dover Publications, October 1, 1979.
- 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.
Printed Resources
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.)