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.

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 nonzero 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:

McAdams, David E. Properties of Zero. 1/5/2019. All Math Words Encyclopedia. Life is a Story Problem LLC.

Revision History

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.)

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