Properties of zero

Pronunciation: /ˈprɒ pər tiz ʌv zɪər oʊ/ ?

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

PropertyDescriptionEquationMore Information
Addition of 00 is the additive identity. Anything plus zero remains unchanged.a + 0 = 0 + a = aAdditive Identity
Subtraction of 0Anything minus zero remains unchanged.a - 0 = anone
Multiplication by 0Anything times zero equals zero.a * 0 = 0 * a = 0Property of Multiplication by Zero
Division by 0Division by zero is undefined.n/aDivision by 0
Exponent of 0Any non-zero number raised to the zero power equals one. Zero raised to the zero power is undefined.a0 = 1, a ≠ 0none
Zero factorialZero factorial is defined to be 1.0! = 1none
IdempotenceZero is idempotent under addition and multiplication(0+0=0), (0·0=0).Idempotence
Table 1: Properties of zero.

Cite this article as:


Properties of zero. 2011-02-14. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/p/propertiesofzero.html.

Image Credits

Revision History


2011-02-14: Added 'More Information' into table of properties. Added Idempotence to table of properties. (McAdams, David.)
2010-10-12: Initial version (McAdams, David.)

All Math Words Encyclopedia is a service of Life is a Story Problem LLC.
Copyright © 2005-2011 Life is a Story Problem LLC. All rights reserved.
Creative Commons License This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License