Zero
0 (zero, ) is a number representing an empty quantity. Adding zero to or subtracting zero from any number leaves that number unchanged. In mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, complex numbers, and algebraic structures. Multiplying any number by 0 results in 0; therefore, division by zero is generally regarded as undefined in arithmetic. Any number to the power of 0 equals 1, except that zero to the power of zero is sometimes regarded as undefined.
As a numerical digit, 0 plays a crucial role in positional notation (i.e., place value notation): it means that the zero position does not increase or decrease the number's total value. For example, 205 in decimal notation means two hundreds, no tens, and five ones, which equals two hundreds plus five ones. The same principle applies in place-value notations that uses a base other than ten, such as binary and hexadecimal notations. This use of zero derives from Indian mathematics, which was transmitted to Europe by medieval Islamic mathematicians and popularized by Fibonacci. It was independently used by the Maya civilization.
Common names for the number 0 in English include zero, nought, naught (), and nil. In contexts where at least one adjacent digit distinguishes it from the letter O, the number is sometimes pronounced as oh or o (). Informal or slang terms for 0 include zilch and zip. Historically, ought, aught (), and cipher have also been used.
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