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0 (zero) is a number representing an empty quantity. Adding (or subtracting) 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 results in 0, and consequently dividing by 0 is generally considered to be undefined 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 (//). 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. In pre-Islamic time the word ṣifr (Arabic صفر) had the meaning "empty". Sifr evolved to mean zero when it was used to translate śūnya (Sanskrit: शून्य) from India. The first known English use of zero was in 1598.

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.

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" (although this is not accurate) and "none" are often used. The British English words "nought" or "naught", and "nil" are also synonymous.

It is often called "oh" in the context of reading out a string of digits, such as telephone numbers, street addresses, credit card numbers, military time, or years. For example, the area code 201 may be pronounced "two oh one", and the year 1907 is often pronounced "nineteen oh seven". The presence of other digits, indicating that the string contains only numbers, avoids confusion with the letter O. For this reason, systems that include strings with both letters and numbers (such as postcodes in the UK) may exclude the use of the letter O.

Slang words for zero include "zip", "zilch", "nada", and "scratch". In the context of sports, "nil" is sometimes used, especially in British English. Several sports have specific words for a score of zero, such as "love" in tennis – possibly from French l'œuf, "the egg" – and "duck" in cricket, a shortening of "duck's egg". "Goose egg" is another general slang term used for zero.

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