Properties of Zero

Pronunciation: /ˈpɹɑp.ər.tiz ʌv ˈzɪər.oʊ/ Explain

The number 0 has several important properties that are useful in algebra. Table 1 gives these properties.

Property	Description	Equation	More Information
Addition of 0	0 is the additive identity. Anything plus zero remains unchanged.	a + 0 = 0 + a = a	Additive Identity
Subtraction of 0	Anything minus zero remains unchanged.	a - 0 = a	none
Multiplication by 0	Anything times zero equals zero.	a · 0 = 0 · a = 0	Property of Multiplication by Zero
Division by 0	Division by zero is undefined.	n/a	Division by 0
Exponent of 0	Any nonzero number raised to the 0 power equals 1. Zero raised to the 0 power is undefined.	a0 = 1, a ≠ 0	none
Zero factorial	Zero factorial is defined to be 1.	0! = 1	none
Idempotence	Zero is idempotent under addition and multiplication.	( 0 + 0 = 0 ), ( 0 · 0 = 0 ).	Idempotence
Table 1: Properties of zero.

Cite this article as:

McAdams, David E. Properties of Zero. 4/29/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/p/propertiesofzero.html.

Revision History

4/29/2019: Changed equations and expressions to new format. (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.)
8/28/2018: Corrected spelling. (McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (McAdams, David E.)
3/5/2010: Initial version. (McAdams, David E.)