0 (number)1

0 (zero;  /ˈziːroʊ/ zeer-oh) is both a number^[1] and the numerical digit used to represent that number in numerals. It plays a central role in mathematics as the additive identity of the integers,real numbers, and many other algebraic structures. As a digit, 0 is used as a placeholder in place value systems. In the English language, 0 may be called zero, nought or (US) naught ( /ˈnɔːt/),nil, or "o". Informal or slang terms for zero include zilch and zip.^[2] Ought or aught ( /ˈɔːt/), have also been used.^[3

As a number

0 is the integer immediately preceding 1. In most cultures, 0 was identified before the idea of negative things that go lower than zero was accepted. Zero is an even number,^[4] because it is divisible by 2. 0 is neither positive nor negative. By some definitions 0 is also a natural number, and then the only natural number not to be positive. Zero is a number which quantifies a count or an amount of null size.

The value, or number, zero is not the same as the digit zero, used in numeral systems using positional notation. Successive positions of digits have higher weights, so inside a numeral the digit zero is used to skip a position and give appropriate weights to the preceding and following digits. A zero digit is not always necessary in a positional number system, for example, in the number 02. In some instances, aleading zero may be used to distinguish a number.

As a year label

Main article: 0 (year)

In the BC calendar era, the year 1 BC is the first year before AD 1; no room is reserved for a year zero. By contrast, in astronomical year numbering, the year 1 BC is numbered 0, the year 2 BC is numbered −1, and so on.^[5]

Names

Main articles: Names for the number 0 and Symbols for zero

In 976 AD the Persian encyclopedist Muhammad ibn Ahmad al-Khwarizmi, in his "Keys of the Sciences", remarked that if, in a calculation, no number appears in the place of tens, then a little circle should be used "to keep the rows". This circle the Arabs called صفر ṣifr, "empty". That was the earliest mention of the name ṣifr that eventually became zero.^[6]

Italian zefiro already meant "west wind" from Latin and Greek zephyrus; this may have influenced the spelling when transcribing Arabic ṣifr.^[7]The Italian mathematician Fibonacci (c.1170–1250), 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, which was contracted to zero in Venetian.

As the decimal zero and its new mathematics spread from the Arab world to Europe in the Middle Ages, words derived from ṣifr and zephyruscame to refer to calculation, as well as to privileged knowledge and secret codes. According to Ifrah, "in thirteenth-century Paris, a 'worthless fellow' was called a '... cifre en algorisme', i.e., an 'arithmetical nothing'."^[7] From ṣifr also came French chiffre = "digit", "figure", "number",chiffrer = "to calculate or compute", chiffré = "encrypted". Today, the word in Arabic is still ṣifr, and cognates of ṣifr are common in the languages of Europe and southwest Asia.

The modern numerical digit 0 is usually written as a circle or ellipse. Traditionally, many print typefaces made the capital letterO more rounded than the narrower, elliptical digit 0.^[8] Typewriters originally made no distinction in shape between O and 0; some models did not even have a separate key for the digit 0. The distinction came into prominence on modern characterdisplays.^[8]

A slashed zero can be used to distinguish the number from the letter. The digit 0 with a dot in the center seems to have originated as an option on IBM 3270 displays and has continued with the some modern computer typefaces such as Andalé Mono. One variation uses a short vertical bar instead of the dot. Some fonts designed for use with computers made one of the capital-O–digit-0 pair more rounded and the other more angular (closer to a rectangle). A further distinction is made in falsification-hindering typeface as used on German car number plates by slitting open the digit 0 on the upper right side. Sometimes the digit 0 is used either exclusively, or not at all, to avoid confusion altogether.