Symmetric Property of Equality

Pronunciation: /sɪˈmɛ.trɪk ˈpɹɑp.ər.ti ʌv ɪˈkwɒl.ɪ.ti/ Explain

The symmetric property of equality for real numbers states that if a = b, then b = a.


Is less than (<) symmetric for real numbers? If it is symmetric, then for all real numbers, if a < b then b < a. Can you find a pair of numbers for which this is not true? Write a proof for your conclusion.


  1. McAdams, David E.. All Math Words Dictionary, symmetric property of equality. 2nd Classroom edition 20150108-4799968. pg 174. Life is a Story Problem LLC. January 8, 2015. Buy the book
  2. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pp 49-50. Thomson, Brooks/Cole. 2005. Buy the book

Cite this article as:

McAdams, David E. Symmetric Property of Equality. 5/7/2019. All Math Words Encyclopedia. Life is a Story Problem LLC.

Revision History

5/7/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
12/10/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
10/5/2007: Initial version. (McAdams, David E.)

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