• German: Null
• Russian: ноль

• German: Nichts
• Russian: ничто

Pronoun

1. nothing

Translations

See also

• aught
• nought
• ought

References

0 (zero) 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, zero is used as a placeholder in place value systems. In the English language, zero may also be called null or nil when a number, "oh" (), "goose egg", or cipher (archaic) when a numeral, and nought or naught in either context.

0 as a number

0 is the integer preceding 1. In most systems, 0 was identified before the idea of 'negative integers' was accepted. Zero is an even number. 0 is neither positive nor negative.

Zero is a number which quantifies a count or an amount of null size; that is, if the number of your brothers is zero, that means the same thing as having no brothers, and if something has a weight of zero, it has no weight. If the difference between the number of pieces in two piles is zero, it means the two piles have an equal number of pieces. Before counting starts, the result can be assumed to be zero; that is the number of items counted before you count the first item and counting the first item brings the result to one. And if there are no items to be counted, zero remains the final result.

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.

0 as a 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 less tall (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.

Distinguishing the digit 0 from the letter O

Traditionally, standard typewriters made no distinction in shape between the letter O and the digit 0; some models did not even have a separate key for the digit 0. The oval (i.e. narrower) digit 0 and more nearly circular letter O together came into prominence on modern character displays, though the distinction was already present in some print typefaces.

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 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.

An alternative, the slashed zero (looking similar to the letter O other than 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 \emptyset, or "∅" (Unicode character U+2205), representing the empty set, as well as to the letter Ø used in several Scandinavian languages. The convention that has the letter O with a slash and the digit 0 without was advocated by SHARE, a prominent IBM user group, 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, The Italian mathematician Fibonacci (c.1170-1250), who grew up in Arab North Africa and is credited with introducing the Hindu decimal system to Europe, used the term zephyrum. This became zefiro in Italian, which was contracted to zero in Venetian, the modern English word.

As the Hindu decimal zero and its new mathematics spread from the Arab world to Europe in the Middle Ages, words derived from sifr 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"."

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.

The Indian scholar Pingala (circa 5th-2nd century BC) used binary numbers in the form of short and long syllables (the latter equal in length to two short syllables), making it similar to Morse code. He and his contemporary Indian scholars used the Sanskrit word śūnya to refer to zero or void.

History of zero

The use of a blank on a counting board to represent 0 dated back in India to 4th century BC. The Mesoamerican Long Count calendar developed in south-central Mexico required the use of zero as a place-holder within its vigesimal (base-20) positional numeral system. Many different glyphs, including this partial quatrefoil—

• In some countries, dialling 0 on a telephone places a call for operator assistance.
• In Braille, the numeral 0 has the same dot configuration as the letter J.
• DVDs that can be played in any region are sometimes referred to as being "region 0"
• In classical music, 0 is very rarely used as a number for a composition: Anton Bruckner wrote a Symphony No. 0 in D minor and a Symphony No. 00; Alfred Schnittke also wrote a Symphony No. 0.
• Roulette wheels usually feature a "0" space (and sometimes also a "00" space), whose presence is ignored when calculating payoffs (thereby allowing the house to win in the long run).
• A chronological prequel of a series may be numbered as 0.
• In Formula One, if the reigning World Champion no longer competes in Formula One in the year following their victory in the title race, 0 is given to one of the drivers of the team that the reigning champion won the title with. This happened in 1993 and 1994, with Damon Hill driving car 0, due to the reigning World Champion (Nigel Mansell and Alain Prost respectively) not competing in the championship.
• In the educational series Schoolhouse Rock!, the song My Hero, Zero is about the use of zero as a placeholder. The song explains that by appending zeroes to a number, it is multiplied by 10 for each one added. This enables mathematicians to create numbers as large as needed.

Quotations

The importance of the creation of the zero mark can never be exaggerated. This giving to airy nothing, not merely a local habitation and a name, a picture, a symbol, but helpful power, is the characteristic of the Hindu race from whence it sprang. It is like coining the Nirvana into dynamos. No single mathematical creation has been more potent for the general on-go of intelligence and power. G.B. Halsted

Dividing by zero...allows you to prove, mathematically, anything in the universe. You can prove that 1+1=42, and from there you can prove that J. Edgar Hoover is a space alien, that William Shakespeare came from Uzbekistan, or even that the sky is polka-dotted. (See appendix A for a proof that Winston Churchill was a carrot.) Charles Seife, from: Zero: The Biography of a Dangerous Idea

...a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it lent to all computations put our arithmetic in the first rank of useful inventions. Pierre-Simon Laplace

The point about zero is that we do not need to use it in the operations of daily life. No one goes out to buy zero fish. It is in a way the most civilized of all the cardinals, and its use is only forced on us by the needs of cultivated modes of thought. Alfred North Whitehead

...a fine and wonderful refuge of the divine spirit--almost an amphibian between being and non-being. Gottfried Leibniz

Notes

References

• Barrow, John D. (2001) The Book of Nothing, Vintage. ISBN 0-09-928845-1.
• Diehl, Richard A. (2004) The Olmecs: America's First Civilization, Thames & Hudson, London.
• Ifrah, Georges (2000) The Universal History of Numbers: From Prehistory to the Invention of the Computer, Wiley. ISBN 0-471-39340-1.
• Kaplan, Robert (2000) The Nothing That Is: A Natural History of Zero, Oxford: Oxford University Press.
• Seife, Charles (2000) Zero: The Biography of a Dangerous Idea, Penguin USA (Paper). ISBN 0-14-029647-6.

See also

• 0
• Negative and non-negative numbers
• Nothing
• Null
• Number theory
• Peano axioms
• Slashed zero
• Hellenistic zero
• Nullar
• Division by zero
• 00

External links

• A History of Zero
• Zero Saga
• The Discovery of the Zero
• The History of Algebra
• Why numbering should start at zero by Edsger Dijkstra
• "Zeroes" Song parody
• "My Hero Zero" Educational children's song

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