0 (number)

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0

Cardinal 0, zero, "oh" (pronounced /ˈoʊ/), nought, naught, nil, null, zilch, nada, o
Ordinal 0th, zeroth, noughth
Factorization 0
Divisors all numbers
Roman numeral N/A
Arabic ٠,0
Bengali ০
Devanāgarī ०
Chinese 〇，零
Japanese numeral 〇，零
Khmer ០
Thai ๐
Binary 0
Octal 0
Duodecimal 0
Hexadecimal 0

0 is both a number 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, oh, null, nil, "o" or nought, dependent on dialect and context.[1]

As number

0 is the integer preceding 1. In most systems, 0 was identified before the idea of negative things that go lower than zero was accepted. Zero is an even number.[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. Almost all historians omit the year zero from the proleptic Gregorian and Julian calendars, but astronomers include it in these same calendars. However, the phrase Year Zero may be used to describe any event considered so significant that it serves as a new base point in time.

As digit

The modern numerical digit 0 is usually written as a circle, an ellipse, or a rounded rectangle. In most modern typefaces, the height of the 0 character is the same as the other digits. However, in typefaces with text figures, the character is often shorter (x-height).

On the seven-segment displays of calculators, watches, and household appliances, 0 is usually written with six line segments, though on some historical calculator models it was written with four line segments.

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 rare instances, a leading 0 may distinguish a number. This appears in roulette in the United States, where '00' is distinct from '0' (a wager on '0' will not win if the ball lands in '00', and vice versa). Sports where competitors are numbered follow this as well; a stock car numbered '07' would be considered distinct from one numbered '7'. This is most common with single-digit numbers.

Distinguishing the digit 0 from the letter O

Traditionally, many print typefaces made the capital letter O more rounded than narrower, elliptical digit 0.[3] 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 character displays.[3]

The digit 0 with a dot in the centre seems to have originated as an option on IBM 3270 displays. Its appearance has continued with the Microsoft Windows typeface Andalé Mono. One variation used a short vertical bar instead of the dot. This could be confused with the Greek letter Theta on a badly focused display, but in practice there was no confusion because theta was not (then) a displayable character and very little used anyway.

An alternative, the slashed zero (looking similar to the letter O except for the slash), was primarily used in hand-written coding sheets before transcription to punched cards or tape, and is also used in old-style ASCII graphic sets descended from the default typewheel on the ASR-33 Teletype. This form is similar to the symbol , or "∅" (Unicode character U+2205), representing the empty set, as well as to the letter Ø used in several Scandinavian languages. Some Burroughs/Unisys equipment displays a digit 0 with a reversed slash.

The opposing convention that has the letter O with a slash and the digit 0 without was advocated by SHARE, a prominent IBM user group,[3] and recommended by IBM for writing FORTRAN programs,[4] and by a few other early mainframe makers; this is even more problematic for Scandinavians because it means two of their letters collide. Others advocated the opposite convention,[3] including IBM for writing Algol programs.[4] Another convention used on some early line printers left digit 0 unornamented but added a tail or hook to the capital O so that it resembled an inverted Q or cursive capital letter-O ().[3]

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). The Texas Instruments TI-99/4A computer featured a more angular capital O and a more rounded digit 0, whereas others made the choice the other way around.

The typeface used on most European vehicle registration plates distinguishes the two symbols partially in this manner (having a more rectangular or wider shape for the capital O than the digit 0), but in several countries a further distinction is made by slitting open the digit 0 on the upper right side (as in German plates using the fälschungserschwerende Schrift, "harder-to-falsify script").

Sometimes the digit 0 is used either exclusively, or not at all, to avoid confusion altogether. For example, confirmation numbers used by Southwest Airlines use only the capital letters O and I instead of the digits 0 and 1, while Canadian postal codes use only the digits 1 and 0 and never the capital letters O and I, although letters and numbers always alternate.

Names

In 976 Muhammad ibn Musa al-Khwarizmi, in his Keys of the Sciences, remarked that if, in a calculation, no number appears in the place of tens, a little circle should be used "to keep the rows." This circle the Arabs called sifr.[5]

The word "zero" came via French zéro from Venetian zero, which (together with cipher) came via Italian zefiro from Arabic صفر, ṣafira = "it was empty", ṣifr = "zero", "nothing".[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 Arab 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 zephyrus came 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.

History

Early history

By the middle of the 2nd millennium BC, the Babylonian mathematics had a sophisticated sexagesimal positional numeral system. The lack of a positional value (or zero) was indicated by a space between sexagesimal numerals. By 300 BC, a punctuation symbol (two slanted wedges) was co-opted as a placeholder in the same Babylonian system. In a tablet unearthed at Kish (dating from about 700 BC), the scribe Bêl-bân-aplu wrote his zeros with three hooks, rather than two slanted wedges.[8]

The Babylonian placeholder was not a true zero because it was not used alone. Nor was it used at the end of a number. Thus numbers like 2 and 120 (2×60), 3 and 180 (3×60), 4 and 240 (4×60), looked the same because the larger numbers lacked a final sexagesimal placeholder. Only context could differentiate them.

Records show that the ancient Greeks seemed unsure about the status of zero as a number. They asked themselves, "How can nothing be something?", leading to philosophical and, by the Medieval period, religious arguments about the nature and existence of zero and the vacuum. The paradoxes of Zeno of Elea depend in large part on the uncertain interpretation of zero.