Properties of One

Pronunciation: /ˈpɹɑp.ər.tiz ʌv wʌn/ Explain

The number 1 has several important properties that are useful in algebra. Table 1 gives these properties.

Property	Description	Equation	More Information
Multiplication by 1	Anything times one equals itself.	a · 1 = 1 · a = a	Property of Multiplication by 1
Division by 1	Anything divided by one remains unchanged.	a / 1 = a	Property of Division by 1
Exponent of 1	Any number raised to the power of 1 equals itself.	a1 = a	none
Idempotence	1 is idempotent under multiplication and exponentiation.	1 · 1 = 1, 11 = 1	Idempotence
Table 1: Properties of one.

Cite this article as:

McAdams, David E. Properties of One. 4/20/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/p/propertiesofone.html.

Revision History

1/5/2019: Corrected copy error. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
12/1/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (McAdams, David E.)
3/5/2010: Initial version. (McAdams, David E.)