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
- 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
- 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
- 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
- Robert R. Stoll. Set Theory and Logic. pp 29-33. Dover Publications. October 1, 1979. Last Accessed 7/9/2018. Buy the book
- 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.)