Equality of Sets

Pronunciation: /ɪˈkwɒl.ɪ.ti ʌv sɛtz/ Explain

Two sets are equal to each other if they contain exactly the same members^[2]. 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

1. McAdams, David E.. All Math Words Dictionary, equality of sets. 2nd Classroom edition 20150108-4799968. pg 70. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. 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
3. 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
4. Robert R. Stoll. Set Theory and Logic. pp 29-33. Dover Publications. October 1, 1979. Last Accessed 7/9/2018. Buy the book
5. Goldberg, Samuel. Probability: An Introduction. pg 5. www.archive.org. Prentice Hall. 1960. Last Accessed 7/9/2018. http://www.archive.org/stream/probailityanintr000991mbp#page/n22/mode/1up/search/equal. 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. Equality of Sets. 4/20/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/e/equal_set.html.

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.)
1/25/2010: Added "References". (McAdams, David E.)
7/15/2008: Added more information. (McAdams, David E.)
7/14/2008: Expanded text. (McAdams, David E.)
3/28/2008: Initial version. (McAdams, David E.)