0
cardinal 0 , zero , & # 34 ; oh & # 34 ; -lrb- -rrb- , nought , naught , nil , null , zilch , nada ordinal 0th , zeroth , noughth factorization 0 divisors all numbers roman numeral n / a arabic ٠ bengali ০ devanāgarī ० chinese 〇 ， 零 japanese numeral 〇 ， 零 khmer ០ thai ๐ binary 0 octal 0 duodecimal 0 hexadecimal 0 0 -lrb- zero -rrb- 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 oh , null , nil , or nought .
<p>
as number
<p>
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 .
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 .
<p>
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 .
<p>
as digit
<p>
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 -lrb- x-height -rrb- .
<p>
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 .
<p>
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 .
<p>
in rare instances , a leading 0 may distinguish a number . this appears in roulette in the united states , where ' 00 ' is distinct from ' 0 ' -lrb- a wager on ' 0 ' will not win if the ball lands in ' 00 ' , and vice versa -rrb- . 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 .
<p>
distinguishing the digit 0 from the letter o
<p>
traditionally , many print typefaces made the capital letter o more rounded than narrower , elliptical digit 0 .
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 .
<p>
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 -lrb- then -rrb- a displayable character and very little used anyway .
<p>
an alternative , the slashed zero -lrb- looking similar to the letter o except for the slash -rrb- , 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 " ∅ " -lrb- unicode character u + 2205 -rrb- , 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 .
<p>
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 , and recommended by ibm for writing fortran programs , 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 , including ibm for writing algol programs .
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 -lrb- \ mathcal o -rrb- .
<p>
some fonts designed for use with computers made one of the capital-o – digit-0 pair more rounded and the other more angular -lrb- closer to a rectangle -rrb- .
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 .
<p>
the typeface used on most european vehicle registration plates distinguishes the two symbols partially in this manner -lrb- having a more rectangular or wider shape for the capital o than the digit 0 -rrb- , but in several countries a further distinction is made by slitting open the digit 0 on the upper right side -lrb- as in german plates using the fälschungserschwerende schrift , " harder-to-falsify script " -rrb- .
<p>
sometimes the digit 0 is used either exclusively , or not at all , to avoid confusion altogether .
for example , 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 .
<p>
names
<p>
in 976 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 , a little circle should be used " to keep the rows . "
this circle the arabs called sifr .
<p>
the word " zero " came via french zéro from venetian zero , which -lrb- together with -rrb- came via italian zefiro from arabic صفر , ṣafira = " it was empty " , ṣifr = " zero " , " nothing " .
<p>
italian zefiro already meant " west wind " from latin and greek zephyrus ; this may have influenced the spelling when transcribing arabic ṣifr .
the italian mathematician fibonacci -lrb- c.1170-1250 -rrb- , 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 .
<p>
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 " . "
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 .
<p>
history
<p>
early history
<p>
by the middle of the 2nd millennium bce , the babylonian mathematics had a sophisticated sexagesimal positional numeral system .
the lack of a positional value -lrb- or zero -rrb- was indicated by a space between sexagesimal numerals .
by 300 bce , a punctuation symbol -lrb- two slanted wedges -rrb- was co-opted as a placeholder in the same babylonian system .
in a tablet unearthed at kish -lrb- dating from about 700 bce -rrb- , the scribe bêl-bân-aplu wrote his zeros with three hooks , rather than two slanted wedges .
<p>
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 -lrb- 2 × 60 -rrb- , 3 and 180 -lrb- 3 × 60 -rrb- , 4 and 240 -lrb- 4 × 60 -rrb- , looked the same because the larger numbers lacked a final sexagesimal placeholder .
only context could differentiate them .
<p>
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 .
<p>
the concept of zero as a number and not merely a symbol for separation is attributed to india where by the 9th century ce practical calculations were carried out using zero , which was treated like any other number , even in case of division .
the indian scholar pingala -lrb- circa 5th-2nd century bce -rrb- used binary numbers in the form of short and long syllables -lrb- the latter equal in length to two short syllables -rrb- , making it similar to morse code .
he and his contemporary indian scholars used the sanskrit word śūnya to refer to zero or void .
<p>
history of zero
<p>
the mesoamerican long count calendar developed in south-central mexico and central america required the use of zero as a place-holder within its vigesimal -lrb- base-20 -rrb- positional numeral system .
many different glyphs , including this partial quatrefoil — — were used as a zero symbol for these long count dates , the earliest of which -lrb- on stela 2 at chiapa de corzo , chiapas -rrb- has a date of 36 bce .
since the eight earliest long count dates appear outside the maya homeland , it is assumed that the use of zero in the americas predated the maya and was possibly the invention of the olmecs .
many of the earliest long count dates were found within the olmec heartland , although the olmec civilization ended by the 4th century bce , several centuries before the earliest known long count dates .
<p>
although zero became an integral part of maya numerals , it did not influence old world numeral systems .
<p>
quipu , a knotted cord device , used in the inca empire and its predecessor societies in the andean region to record accounting and other digital data , is encoded in a base ten positional system .
zero is represented by the absence of a knot in the appropriate position .
<p>
the use of a blank on a counting board to represent 0 dated back in india to 4th century bce .
<p>
in china , counting rods were used for calculation since the 4th century bce .
chinese mathematicians understood negative numbers and zero , though they had no symbol for the latter , until the work of song dynasty mathematician qin jiushao in 1247 established a symbol for zero in china . the nine chapters on the mathematical art , which was mainly composed in the 1st century ce , stated " -lsb- when subtracting -rsb- subtract same signed numbers , add differently signed numbers , subtract a positive number from zero to make a negative number , and subtract a negative number from zero to make a positive number . "
<p>
by 130 ce , ptolemy , influenced by hipparchus and the babylonians , was using a symbol for zero -lrb- a small circle with a long overbar -rrb- within a sexagesimal numeral system otherwise using alphabetic greek numerals .
because it was used alone , not just as a placeholder , this hellenistic zero was perhaps the first documented use of a number zero in the old world .
however , the positions were usually limited to the fractional part of a number -lrb- called minutes , seconds , thirds , fourths , etc . -rrb- & mdash ; they were not used for the integral part of a number .
in later byzantine manuscripts of ptolemy 's syntaxis mathematica -lrb- also known as the almagest -rrb- , the hellenistic zero had morphed into the greek letter omicron -lrb- otherwise meaning 70 -rrb- .
<p>
another zero was used in tables alongside roman numerals by 525 -lrb- first known use by dionysius exiguus -rrb- , but as a word , nulla meaning " nothing , " not as a symbol .
when division produced zero as a remainder , nihil , also meaning " nothing , " was used .
these medieval zeros were used by all future medieval computists -lrb- calculators of easter -rrb- .
an isolated use of the initial , n , was used in a table of roman numerals by bede or a colleague about 725 , a zero symbol .
<p>
in 498 ce , indian mathematician and astronomer aryabhata stated that " sthanam sthanam dasa gunam " or place to place in ten times in value , which may be the origin of the modern decimal-based place value notation .
<p>
the oldest known text to use a decimal place-value system , including a zero , is the jain text from india entitled the lokavibhâga , dated 458 ce .
this text uses sanskrit numeral words for the digits , with words such as the sanskrit word for void for zero .
the first known use of special glyphs for the decimal digits that includes the indubitable appearance of a symbol for the digit zero , a small circle , appears on a stone inscription found at the chaturbhuja temple at gwalior in india , dated 876 ce .
there are many documents on copper plates , with the same small o in them , dated back as far as the sixth century ce , but their authenticity may be doubted .
<p>
the hindu-arabic numerals and the positional number system were introduced to the islamic civilization by al-khwarizmi . al-khwarizmi 's book on arithmetic synthesized greek and hindu knowledge and also contained his own fundamental contribution to mathematics and science including an explanation of the use of zero .
<p>
it was only centuries later , in the 12th century , that the arabic numeral system was introduced to the western world through latin translations of his arithmetic .
<p>
rules of brahmagupta
<p>
the rules governing the use of zero appeared for the first time in brahmagupta 's book brahmasputha siddhanta -lrb- the opening of the universe -rrb- , written in 628 .
here brahmagupta considers not only zero , but negative numbers , and the algebraic rules for the elementary operations of arithmetic with such numbers .
in some instances , his rules differ from the modern standard .
here are the rules of brahmagupta :
<p>
the sum of zero and a negative number is negative .
the sum of zero and a positive number is positive .
the sum of zero and zero is zero .
the sum of a positive and a negative is their difference ; or , if their absolute values are equal , zero .
a positive or negative number when divided by zero is a fraction with the zero as denominator .
zero divided by a negative or positive number is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator .
zero divided by zero is zero .
<p>
in saying zero divided by zero is zero , brahmagupta differs from the modern position .
mathematicians normally do not assign a value to this , whereas computers and calculators sometimes assign nan , which means " not a number . "
moreover , non-zero positive or negative numbers when divided by zero are either assigned no value , or a value of unsigned infinity , positive infinity , or negative infinity .
once again , these assignments are not numbers , and are associated more with computer science than pure mathematics , where in most contexts no assignment is done .
<p>
zero as a decimal digit
<p>
see also : history of the hindu-arabic numeral system .
<p>
positional notation without the use of zero -lrb- using an empty space in tabular arrangements , or the word kha " emptiness " -rrb- is known to have been in use in india from the 6th century .
the earliest certain use of zero as a decimal positional digit dates to the 5th century mention in the text lokavibhaga .
the glyph for the zero digit was written in the shape of a dot , and consequently called bindu -lrb- " dot " -rrb- .
the dot had been used in greece during earlier ciphered numeral periods .
<p>
the hindu-arabic numeral system -lrb- base 10 -rrb- reached europe in the 11th century , via the iberian peninsula through spanish muslims , the moors , together with knowledge of astronomy and instruments like the astrolabe , first imported by gerbert of aurillac .
for this reason , the numerals came to be known in europe as " arabic numerals " .
the italian mathematician fibonacci or leonardo of pisa was instrumental in bringing the system into european mathematics in 1202 , stating :
<p>
after my father 's appointment by his homeland as state official in the customs house of bugia for the pisan merchants who thronged to it , he took charge ; and in view of its future usefulness and convenience , had me in my boyhood come to him and there wanted me to devote myself to and be instructed in the study of calculation for some days .
there , following my introduction , as a consequence of marvelous instruction in the art , to the nine digits of the hindus , the knowledge of the art very much appealed to me before all others , and for it i realized that all its aspects were studied in egypt , syria , greece , sicily , and provence , with their varying methods ; and at these places thereafter , while on business .
i pursued my study in depth and learned the give-and-take of disputation .
but all this even , and the algorism , as well as the art of pythagoras , i considered as almost a mistake in respect to the method of the hindus -lrb- modus indorum -rrb- .
therefore , embracing more stringently that method of the hindus , and taking stricter pains in its study , while adding certain things from my own understanding and inserting also certain things from the niceties of euclid 's geometric art .
i have striven to compose this book in its entirety as understandably as i could , dividing it into fifteen chapters .
almost everything which i have introduced i have displayed with exact proof , in order that those further seeking this knowledge , with its pre-eminent method , might be instructed , and further , in order that the latin people might not be discovered to be without it , as they have been up to now .
if i have perchance omitted anything more or less proper or necessary , i beg indulgence , since there is no one who is blameless and utterly provident in all things .
the nine indian figures are : 9 8 7 6 5 4 3 2 1 .
with these nine figures , and with the sign 0 ... any number may be written .
<p>
here leonardo of pisa uses the phrase " sign 0 , " indicating it is like a sign to do operations like addition or multiplication .
from the 13th century , manuals on calculation -lrb- adding , multiplying , extracting roots , etc . -rrb- became common in europe where they were called algorimus after the persian mathematician al-khwarizmi .
the most popular was written by johannes de sacrobosco , about 1235 and was one of the earliest scientific books to be printed in 1488 .
until the late 15th century , hindu-arabic numerals seem to have predominated among mathematicians , while merchants preferred to use the roman numerals .
in the 16th century , they became commonly used in europe .
<p>
in mathematics
<p>
elementary algebra
<p>
the number 0 is the least non-negative integer .
the natural number following 0 is 1 and no natural number precedes 0 .
the number 0 may or may not be considered a natural number , but it is a whole number and hence a rational number and a real number -lrb- as well as an algebraic number and a complex number -rrb- .
<p>
the number 0 is neither positive nor negative , neither a prime number nor a composite number , nor is it a unit .
it is , however , even -lrb- see evenness of zero -rrb- .
<p>
the following are some basic -lrb- elementary -rrb- rules for dealing with the number 0 .
these rules apply for any real or complex number x , unless otherwise stated .
<p>
addition : x + 0 = 0 + x = x .
that is , 0 is an identity element -lrb- or neutral element -rrb- with respect to addition .
subtraction : x − 0 = x and 0 − x = − x .
multiplication : x · 0 = 0 · x = 0 .
division : = 0 , for nonzero x .
but is undefined , because 0 has no multiplicative inverse , a consequence of the previous rule ; see division by zero .
exponentiation : x0 = x / x = 1 , except that the case x = 0 may be left undefined in some contexts ; see zero to the zero power .
for all positive real x , 0x = 0 .
<p>
the expression , which may be obtained in an attempt to determine the limit of an expression of the form as a result of applying the lim operator independently to both operands of the fraction , is a so-called " indeterminate form " .
that does not simply mean that the limit sought is necessarily undefined ; rather , it means that the limit of , if it exists , must be found by another method , such as l 'hôpital 's rule .
<p>
the sum of 0 numbers is 0 , and the product of 0 numbers is 1 .
the factorial 0 ! evaluates to 1 .
<p>
other branches of mathematics
<p>
in set theory , 0 is the cardinality of the empty set : if one does not have any apples , then one has 0 apples .
in fact , in certain axiomatic developments of mathematics from set theory , 0 is defined to be the empty set .
when this is done , the empty set is the von neumann cardinal assignment for a set with no elements , which is the empty set .
the cardinality function , applied to the empty set , returns the empty set as a value , thereby assigning it 0 elements .
also in set theory , 0 is the least ordinal number , corresponding to the empty set viewed as a well-ordered set .
in propositional logic , 0 may be used to denote the truth value false .
in abstract algebra , 0 is commonly used to denote a zero element , which is a neutral element for addition -lrb- if defined on the structure under consideration -rrb- and an absorbing element for multiplication -lrb- if defined -rrb- .
in lattice theory , 0 may denote the bottom element of a bounded lattice .
in category theory , 0 is sometimes used to denote an initial object of a category .
<p>
related mathematical terms
<p>
a zero of a function f is a point x in the domain of the function such that f -lrb- x -rrb- = 0 .
when there are finitely many zeros these are called the roots of the function .
see also zero -lrb- complex analysis -rrb- for zeros of a holomorphic function .
the zero function -lrb- or zero map -rrb- on a domain d is the constant function with 0 as its only possible output value , i.e. , the function f defined by f -lrb- x -rrb- = 0 for all x in d. a particular zero function is a zero morphism in category theory ; e.g. , a zero map is the identity in the additive group of functions .
the determinant on non-invertible square matrices is a zero map .
<p>
in science
<p>
physics
<p>
the value zero plays a special role for many physical quantities .
for some quantities , the zero level is naturally distinguished from all other levels , whereas for others it is more or less arbitrarily chosen .
for example , on the kelvin temperature scale , zero is the coldest possible temperature -lrb- negative temperatures exist but are not actually colder -rrb- , whereas on the celsius scale , zero is arbitrarily defined to be at the freezing point of water .
measuring sound intensity in decibels or phons , the zero level is arbitrarily set at a reference value — for example , at a value for the threshold of hearing .
in physics , the zero-point energy is the lowest possible energy that a quantum mechanical physical system may possess and is the energy of the ground state of the system .
<p>
chemistry
<p>
zero has been proposed as the atomic number of the theoretical element tetraneutron .
it has been shown that a cluster of four neutrons may be stable enough to be considered an atom in its own right .
this would create an element with no protons and no charge on its nucleus .
<p>
as early as 1926 , professor andreas von antropoff coined the term neutronium for a conjectured form of matter made up of neutrons with no protons , which he placed as the chemical element of atomic number zero at the head of his new version of the periodic table .
it was subsequently placed as a noble gas in the middle of several spiral representations of the periodic system for classifying the chemical elements .
it is at the centre of the chemical galaxy -lrb- 2005 -rrb- .
<p>
medical science
<p>
patient zero is the initial patient in the population sample of an epidemiological investigation .
<p>
in computer science
<p>
numbering from 1 or 0
<p>
the most common practice throughout human history has been to start counting at one .
nevertheless , in computer science zero is often used as the starting point .
for example , in the vast majority of programming languages , the elements of an array are numbered starting from 0 by default .
the popularity of the c programming language in the 1980s has made this approach common .
<p>
one advantage of this convention is in the use of modular arithmetic .
every integer is congruent modulo n to one of the numbers 0 , 1 , 2 , ... , , where .
because of this , many arithmetic concepts -lrb- such as hash tables -rrb- are more elegantly expressed in code when the array starts at zero .
<p>
a second advantage of zero-based array indexes is that this can improve efficiency under certain circumstances .
to illustrate , suppose a is the memory address of the first element of an array , and i is the index of the desired element .
in this fairly typical scenario , it is quite common to want the address of the desired element .
if the index numbers count from 1 , the desired address is computed by this expression :
<p>
a + s \ times -lrb- i-1 -rrb- \ , \ !
<p>
where s is the size of each element .
in contrast , if the index numbers count from 0 , the expression becomes this :
<p>
a + s \ times i \ , \ !
<p>
this simpler expression can be more efficient to compute in certain situations .
<p>
note , however , that a language wishing to index arrays from 1 could simply adopt the convention that every " array address " is represented by a ′ = a – s ; that is , rather than using the address of the first array element , such a language would use the address of an imaginary element located immediately before the first actual element .
the indexing expression for a 1-based index would be the following :
<p>
a ' + s \ times i \ , \ !
<p>
hence , the efficiency benefit of zero-based indexing is not inherent , but is an artifact of the decision to represent an array by the address of its first element .
<p>
a third advantage is that ranges are more elegantly expressed as the half-open interval , -lsb- 0 , n -rrb- , as opposed to the closed interval , -lsb- 1 , n -rsb- , because empty ranges often occur as input to algorithms -lrb- which would be tricky to express with the closed interval without resorting to obtuse conventions like -lsb- 1,0 -rsb- -rrb- .
on the other hand , closed intervals occur in mathematics because it is often necessary to calculate the terminating condition -lrb- which would be impossible in some cases because the half-open interval is n't always a closed set -rrb- which would have a subtraction by 1 everywhere .
<p>
this situation can lead to some confusion in terminology .
in a zero-based indexing scheme , the first element is " element number zero " ; likewise , the twelfth element is " element number eleven " .
therefore , an analogy from the ordinal numbers to the quantity of objects numbered appears ; the highest index of n objects will be and referred to the nth element .
for this reason , the first element is often referred to as the zeroth element to avoid confusion .
<p>
null value
<p>
in databases a field can have a null value .
this is equivalent to the field not having a value .
for numeric fields it is not the value zero .
for text fields this is not blank nor the empty string .
the presence of null values leads to three-valued logic .
no longer is a condition either true or false , but it can be undetermined .
any computation including a null value delivers a null result .
asking for all records with value 0 or value not equal 0 will not yield all records , since the records with value null are excluded .
<p>
null pointer
<p>
a null pointer is a pointer in a computer program that does not point to any object or function .
in c , the integer constant 0 is converted into the null pointer at compile time when it appears in a pointer context , and so 0 is a standard way to refer to the null pointer in code .
however , the internal representation of the null pointer may be any bit pattern -lrb- possibly different values for different data types -rrb- .
<p>
-lrb- note that on most common architectures , the null pointer is represented internally the same way an integer of the same byte width having a value of zero is represented , so c compilers on such systems perform no actual conversion . -rrb-
<p>
negative zero
<p>
in mathematics -0 = 0 = + 0 , both − 0 and + 0 represent the exact same number , i.e. , there is no “ negative zero ” distinct from zero .
in some signed number representations -lrb- but not the two 's complement representation used to represent integers in most computers today -rrb- and most floating point number representations , zero has two distinct representations , one grouping it with the positive numbers and one with the negatives ; this latter representation is known as negative zero .
<p>
in other fields
<p>
in some countries and some company phone networks , dialing 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 & # 34 ; region 0 & # 34 ; 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 & # 34 ; 0 & # 34 ; space -lrb- and sometimes also a & # 34 ; 00 & # 34 ; space -rrb- , whose presence is ignored when calculating payoffs -lrb- thereby allowing the house to win in the long run -rrb- .
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 -lrb- nigel mansell and alain prost respectively -rrb- 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 zeros to a number , it is multiplied by 10 for each one added .
this enables mathematicians to create numbers as large as needed .
<p>
quotations
<p>
see also
<p>
grammatical number number theory peano axioms
<p>
notes
<p>
references
<p>
barrow , john d. -lrb- 2001 -rrb- the book of nothing , vintage .
isbn 0-09-928845-1 .
diehl , richard a. -lrb- 2004 -rrb- the olmecs : america 's first civilization , thames & # 38 ; hudson , london .
ifrah , georges -lrb- 2000 -rrb- the universal history of numbers : from prehistory to the invention of the computer , wiley .
isbn 0-471-39340-1 .
kaplan , robert -lrb- 2000 -rrb- the nothing that is : a natural history of zero , oxford : oxford university press .
seife , charles -lrb- 2000 -rrb- zero : the biography of a dangerous idea , penguin usa -lrb- paper -rrb- .
isbn 0-14-029647-6 .
bourbaki , nicolas -lrb- 1998 -rrb- .
elements of the history of mathematics .
berlin , heidelberg , and new york : springer-verlag .
isbn 3540647678 .
isaac asimov article & # 34 ; nothing counts & # 34 ; in & # 34 ; asimov on numbers & # 34 ; pocket books , 1978
<p>
external links
<p>
a history of zero zero saga the discovery of the zero the history of algebra edsger w. dijkstra : why numbering should start at zero , 192 -lrb- pdf of a handwritten manuscript -rrb- " my hero zero " educational children & # 39 ; s song in schoolhouse rock
