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