0 (zero) is a number representing an empty quantity. Adding 0 to any number leaves that number unchanged. In mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and complex numbers, as well as other algebraic structures. Multiplying any number by 0 has the result 0, and consequently, division by zero has no meaning in arithmetic.
As a numerical digit, 0 plays a crucial role in decimal notation: it indicates that the power of ten corresponding to the place containing a 0 does not contribute to the total. For example, "205" in decimal means two hundreds, no tens, and five ones. The same principle applies in place-value notations that uses a base other than ten, such as binary and hexadecimal. The modern use of 0 in this manner derives from Indian mathematics that was transmitted to Europe via medieval Islamic mathematicians and popularized by Fibonacci. It was independently used by the Maya.
Common names for the number 0 in English include zero, nought, naught (/nɔːt/), 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 (/oʊ/). Informal or slang terms for 0 include zilch and zip. Historically, ought, aught (/ɔːt/), and cipher have also been used.
The word zero came into the English language via French zéro from the Italian zero, a contraction of the Venetian zevero form of Italian zefiro via ṣafira or ṣifr.[1] In pre-Islamic time the word ṣifr (Arabic صفر) had the meaning "empty".[2] Sifr evolved to mean zero when it was used to translate śūnya (Sanskrit: शून्य) from India.[2] The first known English use of zero was in 1598.[3]
The Italian mathematician Fibonacci (c. 1170 – c. 1250), who grew up in North Africa and is credited with introducing the decimal system to Europe, used the term zephyrum. This became zefiro in Italian, and was then contracted to zero in Venetian. The Italian word zefiro was already in existence (meaning "west wind" from Latin and Greek Zephyrus) and may have influenced the spelling when transcribing Arabic ṣifr.[4]
Depending on the context, there may be different words used for the number zero, or the concept of zero. For the simple notion of lacking, the words "nothing" and "none" are often used. The British English words "nought" or "naught", and "nil" are also synonymous.[5][6]