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. | a^{0} = 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. |
# | A | B | C | D |
E | F | G | H | I |
J | K | L | M | N |
O | P | Q | R | S |
T | U | V | W | X |
Y | Z |
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