Zero (0) is both a
number and a numeral
?. The number zero is the size of the empty
set: if you don't have any apples, then you have zero apples. The numeral or digit zero is used in [positional number systems]
?, where the position of a digit signifies its value, with successive postitions having higher values, and the digit zero is used to skip a position. This use was introduced into
mathematics relatively late, during the early
800s in
Indian books.
Prior number systems, such as the
Babylonian or
Greek, were not positional and did not use the digit zero at all, but still succeeded quite well for everyday purposes. The number zero was not accepted until later still.
The following are some basic rules for dealing with the number zero.
These rules apply for any complex number x, unless otherwise stated.
- Addition: x + 0 = x and 0 + x = x. (That is, 0 is an identity element with respect to addition.)
- Subtraction: x - 0 = x and 0 - x = -x.
- Multiplication: x × 0 = 0 and 0 × x = 0.
- Division: 0 / x = 0, for nonzero x. But x / 0 is undefined, because 0 has no multiplicative inverse.
- Exponentiation: x0 = 1, except that the case x = 0 may be left undefined in some contexts. For all positive x, 0x = 0.
/Talk
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