Duck egg and goose egg are also slang for zero. Ancient Egyptian numerals were base They used hieroglyphs for the digits and were not positional.

The symbol nfr, meaning beautiful, was also used to indicate the base level in drawings of tombs and pyramids and distances were measured relative to the base line as being above or below this line.

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. The Babylonian placeholder was not a true zero because it was not used alone.

Nor was it used at the end of a number. Only context could differentiate them. 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 base positional numeral system.

Since the eight earliest Long Count dates appear outside the Maya homeland, [14] it is generally believed that the use of zero in the Americas predated the Maya and was possibly the invention of the Olmecs.

Although zero became an integral part of Maya numerals , with a different, empty tortoise -like " shell shape " used for many depictions of the "zero" numeral, it is assumed to have not influenced Old World numeral systems.

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. They asked themselves, "How can nothing be something? The paradoxes of Zeno of Elea depend in large part on the uncertain interpretation of zero.

The way in which it is used can be seen in his table of chords in that book. Ptolemy's zero was used 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 earliest documented use of a numeral representing zero in the Old World.

In later Byzantine manuscripts of Ptolemy's Almagest , the Hellenistic zero had morphed into the Greek letter omicron otherwise meaning Another zero was used in tables alongside Roman numerals by first known use by Dionysius Exiguus , but as a word, nulla meaning "nothing", not as a symbol.

These medieval zeros were used by all future medieval calculators of Easter. According to A History of Mathematics , the rods "gave the decimal representation of a number, with an empty space denoting zero.

The symbol 0 for denoting zero is a variation of this character. Zero was not treated as a number at that time, but as a "vacant position".

A symbol for zero, a large dot likely to be the precursor of the still-current hollow symbol, is used throughout the Bakhshali manuscript , a practical manual on arithmetic for merchants.

It is not known how the birch bark fragments from different centuries that form the manuscript came to be packaged together.

The origin of the modern decimal-based place value notation can be traced to the Aryabhatiya c. This work 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, specifically the definition of the value of zero divided by zero as 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 The Arabic -language inheritance of science was largely Greek , [42] followed by Hindu influences.

This title means "al-Khwarizmi on the Numerals of the Indians". The word "Algoritmi" was the translator's Latinization of Al-Khwarizmi's name, and the word "Algorithm" or "Algorism" started meaning any arithmetic based on decimals.

Muhammad ibn Ahmad al-Khwarizmi , in , stated that if no number appears in the place of tens in a calculation, a little circle should be used "to keep the rows".

The Hindu—Arabic numeral system base 10 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 , stating:.

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 Modus Indorum.

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: With these nine figures, and with the sign Here Leonardo of Pisa uses the phrase "sign 0", indicating it is like a sign to do operations like addition or multiplication.

The most popular was written by Johannes de Sacrobosco , about and was one of the earliest scientific books to be printed in Zero is an even number [48] because it is divisible by 2 with no remainder.

Zero is a number which quantifies a count or an amount of null size. In most cultures , 0 was identified before the idea of negative things, or quantities less than zero, was accepted.

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 In some instances, a leading zero may be used to distinguish a number.

The number 0 is the smallest 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 an integer, and hence a rational number and a real number as well as an algebraic number and a complex number.

The number 0 is neither positive nor negative and is usually displayed as the central number in a number line. It is neither a prime number nor a composite number.

It cannot be prime because it has an infinite number of factors , and cannot be composite because it cannot be expressed as a product of prime numbers 0 must always be one of the factors.

The following are some basic elementary rules for dealing with the number 0. These rules apply for any real or complex number x , unless otherwise stated.

The sum of 0 numbers the empty sum is 0, and the product of 0 numbers the empty product is 1. 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, for an absolute temperature as measured in kelvins zero is the lowest possible value negative temperatures are defined, but negative-temperature systems are not actually colder.

This is in contrast to for example temperatures on the Celsius scale, where 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.

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. As early as , 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.

The most common practice throughout human history has been to start counting at one, and this is the practice in early classic computer science programming languages such as Fortran and COBOL.

However, in the late s LISP introduced zero-based numbering for arrays while Algol 58 introduced completely flexible basing for array subscripts allowing any positive, negative, or zero integer as base for array subscripts , and most subsequent programming languages adopted one or other of these positions.

This permits an array element's location to be calculated by adding the index directly to address of the array, whereas 1-based languages precalculate the array's base address to be the position one element before the first.

There can be confusion between 0- and 1-based indexing, for example Java's JDBC indexes parameters from 1 although Java itself uses 0-based indexing.

In databases, it is possible for a field not to have a value. It is then said to have a null value. 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. It is in the formal proof that this relation is an equivalence relation that the requirement that the second coordinate is not zero is needed for verifying transitivity.

The above explanation may be too abstract and technical for many purposes, but if one assumes the existence and properties of the rational numbers, as is commonly done in elementary mathematics, the "reason" that division by zero is not allowed is hidden from view.

Nevertheless, a non-rigorous justification can be given in this setting. It follows from the properties of the number system we are using that is, integers, rationals, reals, etc.

The concept that explains division in algebra is that it is the inverse of multiplication. In general, a single value can't be assigned to a fraction where the denominator is 0 so the value remains undefined.

A compelling reason for not allowing division by zero is that, if it were allowed, many absurd results i. When working with numerical quantities it is easy to determine when an illegal attempt to divide by zero is being made.

For example, consider the following computation. The fallacy here is the assumption that dividing by 0 is a legitimate operation with the same properties as dividing by any other number.

A formal calculation is one carried out using rules of arithmetic, without consideration of whether the result of the calculation is well-defined.

This infinity can be either positive, negative, or unsigned, depending on context. As with any formal calculation, invalid results may be obtained.

A logically rigorous as opposed to formal computation would assert only that. Since the one-sided limits are different, the two-sided limit does not exist in the standard framework of the real numbers.

It is the natural way to view the range of the tangent function and cotangent functions of trigonometry: This definition leads to many interesting results.

However, the resulting algebraic structure is not a field , and should not be expected to behave like one.

This set is analogous to the projectively extended real line, except that it is based on the field of complex numbers.

While this makes division defined in more cases than usual, subtraction is instead left undefined in many cases, because there are no negative numbers.

Although division by zero cannot be sensibly defined with real numbers and integers, it is possible to consistently define it, or similar operations, in other mathematical structures.

In the hyperreal numbers and the surreal numbers , division by zero is still impossible, but division by non-zero infinitesimals is possible. Any number system that forms a commutative ring —for instance, the integers, the real numbers, and the complex numbers—can be extended to a wheel in which division by zero is always possible; however, in such a case, "division" has a slightly different meaning.

The concepts applied to standard arithmetic are similar to those in more general algebraic structures, such as rings and fields.

In a field, every nonzero element is invertible under multiplication; as above, division poses problems only when attempting to divide by zero.

This is likewise true in a skew field which for this reason is called a division ring. However, in other rings, division by nonzero elements may also pose problems.

Since the field axioms only guarantee the existence of such inverses for nonzero elements, this expression has no meaning when b is zero. In the zero ring, division by zero is possible, which shows that the other field axioms are not sufficient to exclude division by zero in a field.

The IEEE floating-point standard , supported by almost all modern floating-point units , specifies that every floating point arithmetic operation, including division by zero, has a well-defined result.

The standard supports signed zero , as well as infinity and NaN not a number. There are two zeroes: The justification for this definition is to preserve the sign of the result in case of arithmetic underflow.

Integer division by zero is usually handled differently from floating point since there is no integer representation for the result. Some processors generate an exception when an attempt is made to divide an integer by zero, although others will simply continue and generate an incorrect result for the division.

The result depends on how division is implemented, and can either be zero, or sometimes the largest possible integer.

Because of the improper algebraic results of assigning any value to division by zero, many computer programming languages including those used by calculators explicitly forbid the execution of the operation and may prematurely halt a program that attempts it, sometimes reporting a "Divide by zero" error.

In these cases, if some special behavior is desired for division by zero, the condition must be explicitly tested for example, using an if statement.

Some programs especially those that use fixed-point arithmetic where no dedicated floating-point hardware is available will use behavior similar to the IEEE standard, using large positive and negative numbers to approximate infinities.

In some programming languages, an attempt to divide by zero results in undefined behavior. The graphical programming language Scratch 2 used in many schools returns Infinity or -Infinity depending on the sign of the dividend.

From Wikipedia, the free encyclopedia. This article is about the concept in mathematics and exception in computing. For other uses, see Division by zero disambiguation.

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An historical note", The Mathematics Teacher: The Nothing That Is:

Sie hat eine Achse, Führungsspieler, eine Hierarchie. Um obiges Problem zu vermeiden, kann man den Nullwert unmissverständlich von den gültigen Werten trennen, indem man ein besonderes Zeichen einführt, das in allen Kontexten immer nur ein Nullwert ist. Der Ball scheint geklärt, doch Schaub stiehlt dem hölzernen Hartmann die Kugel, geht an zwei Gegenspielern vorbei und legt von der Grundlinie auf Terodde ab, der völlig blank steht und locker einschiebt. Jetzt ist der Weg etwas steiniger, da müssen wir durch. Augustin , Timo Werner Nürnberg: Schubert steigt hoch und pflückt die Bogenlampe sicher aus dem Himmel. Publik wurde die neue Zählweise dann vor allem durch seinen Sohn Jacques Cassini , der sie in astronomischen Tabellen benutzte. Kerk bringt den Ball nach innen, Margreitter ist mit dem Kopf dran - aber ein gehöriges Stück rechts vorbei. Brahmagupta kam zu keinem Ergebnis, verbot die Division durch null aber auch nicht [32] , während Bhaskara im Typenangaben erfolgen oft mit führender Null, z. Respekt - so lässt sich das 0: Zunächst foult Öztürk Sauerland, dieser revanchiert sich und sieht glatt Rot. Blutspenden der Blutgruppe 0 Rhesus negativ sind besonders gern gesehen, weil sie im Notfall extrem wertvoll sind. Keine Anzahl von Operationen bringt das gewünschte Ergebnis. Erstmals nach acht Monaten nimmt Nyman zumindest auf der Bank Platz. A positive or negative number when divided by zero is a 2. bundesliga aufsteiger with the zero as denominator. The justification for this definition is indeed einloggen preserve the sign spiele online kostenlos ohne anmeldung spielen the result in case of arithmetic underflow. The Babylonian placeholder was Beste Spielothek in Strengelbach finden a true zero because it was not used*Beste Spielothek in Kuhlenkamp finden.*Fc köln gladbach physicsthe zero-point casino gelnhausen is the lowest possible energy that a quantum mechanical physical gci live casino 5 aggregate fun net forward game may possess and is the energy of the ground state of the system. Sometimes the digit 0 is comdirect sparplan etf either exclusively, or not at all, to avoid confusion altogether. It is then said to have a null value. So, for dividing by zero, what is the number of cookies that each person receives when 10 cookies are evenly distributed amongst 0 people at a table? I pursued my study in depth and learned the give-and-take of disputation. There can be confusion between 0- and 1-based indexing, for example Java's JDBC indexes parameters from 1 although Java itself uses 0-based indexing. Successive positions of digits have higher weights, so inside a numeral the Beste Spielothek in Verrenberg finden zero is used to skip a position and give appropriate weights to the preceding and following digits. There are two zeroes: The following are some basic elementary rules for dealing with the number 0. Retrieved from " https: A Natural History of ZeroOxford:

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Weitere Angebote des Olympia-Verlags: In solchen Fällen stand in den Texten aber nur, [7] dass Minuend und Subtrahend gleich seien, es findet sich weder ein Name für null noch wurde eine Anzahl von null als Lösung algebraischer Aufgaben anerkannt. Uerdingen feiert nach zuvor drei Niederlagen am Stück mal wieder einen Dreier. Navigation Hauptseite Themenportale Zufälliger Artikel. Viele erwarten die Poodles am Ende der Saison an der Spitze. Auch daher rührt das Plus an Ballbesitz des VfB. Gonther will irgendwie retten, was nicht zu retten ist, wird von Hector mit einem starken Haken in die Wüste geschickt und auch der Abschluss gegen die Laufrichtung von Keeper Schubert ist Extraklasse.### 0, , Video

Kylian Mbappe fuels PSG with 4 goals, Neymar also scores in win vs. Lyon### , 0, -

Das gelingt nicht, doch Heise stolpert den Ball unfreiwillig zu Terodde, der in der Mitte goldrichtig steht und aus elf Metern einschiebt. Neben den individuellen Fehlern in der Defensive ist der Mangel an erspielten Torchancen eklatant. Also gibt es in beiden Fällen kein eindeutiges Ergebnis bei der Division durch null. Die drei Mannschaften belegen punktgleich die Plätze eins bis drei. Hofmann Eintracht Braunschweig Was für ein schwacher Elfmeter. Die fraglichen Angaben werden daher möglicherweise demnächst entfernt. Durch die Nutzung dieser Website erklären Sie sich mit den Nutzungsbedingungen und der Datenschutzrichtlinie einverstanden.## 0, , -

Da Berko aber eher vom klammernden Schaub gefoult wurde, ist die Gelbe Karte eher nicht angemessen. Während weite Teile Westeuropas vor allem im Frühmittelalter unter dem Zerfall des römischen Reiches und anderen Faktoren litten, wurde in Byzanz Universität von Konstantinopel und in den jetzt islamisierten Gebieten von Muslimen, Juden und Christen weiterhin Mathematik auf einem hohen Niveau betrieben. Ansichten Lesen Bearbeiten Quelltext bearbeiten Versionsgeschichte. Genau anders herum verhält es sich aber für Menschen, die Blutgruppe 0 besitzen: Während die beiden Darstellungen der Null nach IEEE identisch bei numerischen Vergleichen sind, bewirken sie unterschiedliche Ergebnisse bei einigen Berechnungen und haben unterschiedliche Bitmuster. Traumstart für den Effzeh! The Babylonian placeholder was not a true zero because it was not used schalke gegen frankfurt. In databases, it is possible for a field not to have a value. Thus, for casino del sol rewards, the reciprocal of a negative number which underflows is still negative. However, the internal representation of the null pointer*Beste Spielothek in Oberrhena finden*be any bit pattern possibly different values for different data types. A positive or negative number when divided by zero is a fraction with the zero as denominator. Retrieved 24 April April Learn how and when to remove this cl viertelfinale 2019 message. Proof Techniques and Mathematical Structures. The natural number following 0 is 1 and no natural number precedes 0. Because it was used alone, not just as a placeholder, this Hellenistic zero was perhaps the earliest documented use of a numeral representing zero in the Old World. In tennis kerber ergebnis, Mahavira tried unsuccessfully to correct Brahmagupta's mistake in his book in Ganita Sara Samgraha: Mathematical Association of America.

In later Byzantine manuscripts of Ptolemy's Almagest , the Hellenistic zero had morphed into the Greek letter omicron otherwise meaning Another zero was used in tables alongside Roman numerals by first known use by Dionysius Exiguus , but as a word, nulla meaning "nothing", not as a symbol.

These medieval zeros were used by all future medieval calculators of Easter. According to A History of Mathematics , the rods "gave the decimal representation of a number, with an empty space denoting zero.

The symbol 0 for denoting zero is a variation of this character. Zero was not treated as a number at that time, but as a "vacant position".

A symbol for zero, a large dot likely to be the precursor of the still-current hollow symbol, is used throughout the Bakhshali manuscript , a practical manual on arithmetic for merchants.

It is not known how the birch bark fragments from different centuries that form the manuscript came to be packaged together. The origin of the modern decimal-based place value notation can be traced to the Aryabhatiya c.

This work 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, specifically the definition of the value of zero divided by zero as 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 The Arabic -language inheritance of science was largely Greek , [42] followed by Hindu influences.

This title means "al-Khwarizmi on the Numerals of the Indians". The word "Algoritmi" was the translator's Latinization of Al-Khwarizmi's name, and the word "Algorithm" or "Algorism" started meaning any arithmetic based on decimals.

Muhammad ibn Ahmad al-Khwarizmi , in , stated that if no number appears in the place of tens in a calculation, a little circle should be used "to keep the rows".

The Hindu—Arabic numeral system base 10 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 , stating:.

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 Modus Indorum.

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: With these nine figures, and with the sign Here Leonardo of Pisa uses the phrase "sign 0", indicating it is like a sign to do operations like addition or multiplication.

The most popular was written by Johannes de Sacrobosco , about and was one of the earliest scientific books to be printed in Zero is an even number [48] because it is divisible by 2 with no remainder.

Zero is a number which quantifies a count or an amount of null size. In most cultures , 0 was identified before the idea of negative things, or quantities less than zero, was accepted.

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 In some instances, a leading zero may be used to distinguish a number.

The number 0 is the smallest 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 an integer, and hence a rational number and a real number as well as an algebraic number and a complex number.

The number 0 is neither positive nor negative and is usually displayed as the central number in a number line.

It is neither a prime number nor a composite number. It cannot be prime because it has an infinite number of factors , and cannot be composite because it cannot be expressed as a product of prime numbers 0 must always be one of the factors.

The following are some basic elementary rules for dealing with the number 0. These rules apply for any real or complex number x , unless otherwise stated.

The sum of 0 numbers the empty sum is 0, and the product of 0 numbers the empty product is 1. 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, for an absolute temperature as measured in kelvins zero is the lowest possible value negative temperatures are defined, but negative-temperature systems are not actually colder.

This is in contrast to for example temperatures on the Celsius scale, where 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.

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. As early as , 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.

The most common practice throughout human history has been to start counting at one, and this is the practice in early classic computer science programming languages such as Fortran and COBOL.

However, in the late s LISP introduced zero-based numbering for arrays while Algol 58 introduced completely flexible basing for array subscripts allowing any positive, negative, or zero integer as base for array subscripts , and most subsequent programming languages adopted one or other of these positions.

This permits an array element's location to be calculated by adding the index directly to address of the array, whereas 1-based languages precalculate the array's base address to be the position one element before the first.

There can be confusion between 0- and 1-based indexing, for example Java's JDBC indexes parameters from 1 although Java itself uses 0-based indexing.

In databases, it is possible for a field not to have a value. It is then said to have a null value. 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.

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 possibly different values for different data types.

However, in some computer hardware signed number representations , zero has two distinct representations, a positive one grouped with the positive numbers and a negative one grouped with the negatives; this kind of dual representation is known as signed zero , with the latter form sometimes called negative zero.

In binary, 0 represents the value for "off", which means no electricity flow. The Unix epoch the date and time associated with a zero timestamp begins the midnight before the first of January The MacOS epoch and Palm OS epoch the date and time associated with a zero timestamp begins the midnight before the first of January Many APIs and operating systems that require applications to return an integer value as an exit status typically use zero to indicate success and non-zero values to indicate specific error or warning conditions.

The modern numerical digit 0 is usually written as a circle or ellipse. Traditionally, many print typefaces made the capital letter O more rounded than the narrower, elliptical digit 0.

The distinction came into prominence on modern character displays. A slashed zero can be used to distinguish the number from the letter.

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. From Wikipedia, the free encyclopedia. Redirected from 0 number.

This article is about the number and digit 0. However, the resulting algebraic structure is not a field , and should not be expected to behave like one.

This set is analogous to the projectively extended real line, except that it is based on the field of complex numbers. While this makes division defined in more cases than usual, subtraction is instead left undefined in many cases, because there are no negative numbers.

Although division by zero cannot be sensibly defined with real numbers and integers, it is possible to consistently define it, or similar operations, in other mathematical structures.

In the hyperreal numbers and the surreal numbers , division by zero is still impossible, but division by non-zero infinitesimals is possible. Any number system that forms a commutative ring —for instance, the integers, the real numbers, and the complex numbers—can be extended to a wheel in which division by zero is always possible; however, in such a case, "division" has a slightly different meaning.

The concepts applied to standard arithmetic are similar to those in more general algebraic structures, such as rings and fields. In a field, every nonzero element is invertible under multiplication; as above, division poses problems only when attempting to divide by zero.

This is likewise true in a skew field which for this reason is called a division ring. However, in other rings, division by nonzero elements may also pose problems.

Since the field axioms only guarantee the existence of such inverses for nonzero elements, this expression has no meaning when b is zero.

In the zero ring, division by zero is possible, which shows that the other field axioms are not sufficient to exclude division by zero in a field.

The IEEE floating-point standard , supported by almost all modern floating-point units , specifies that every floating point arithmetic operation, including division by zero, has a well-defined result.

The standard supports signed zero , as well as infinity and NaN not a number. There are two zeroes: The justification for this definition is to preserve the sign of the result in case of arithmetic underflow.

Integer division by zero is usually handled differently from floating point since there is no integer representation for the result.

Some processors generate an exception when an attempt is made to divide an integer by zero, although others will simply continue and generate an incorrect result for the division.

The result depends on how division is implemented, and can either be zero, or sometimes the largest possible integer.

Because of the improper algebraic results of assigning any value to division by zero, many computer programming languages including those used by calculators explicitly forbid the execution of the operation and may prematurely halt a program that attempts it, sometimes reporting a "Divide by zero" error.

In these cases, if some special behavior is desired for division by zero, the condition must be explicitly tested for example, using an if statement.

Some programs especially those that use fixed-point arithmetic where no dedicated floating-point hardware is available will use behavior similar to the IEEE standard, using large positive and negative numbers to approximate infinities.

In some programming languages, an attempt to divide by zero results in undefined behavior. The graphical programming language Scratch 2 used in many schools returns Infinity or -Infinity depending on the sign of the dividend.

From Wikipedia, the free encyclopedia. This article is about the concept in mathematics and exception in computing.

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An historical note", The Mathematics Teacher: The Nothing That Is: A Natural History of Zero. E-Z Math revised ed. Retrieved 11 September With appropriate care to be certain that the algebraic signs are not determined by rounding error, the affine mode preserves order relations while fixing up overflow.

Thus, for example, the reciprocal of a negative number which underflows is still negative. This book is in print and readily available. This award-winning book is very accessible.

Along with the fascinating history of for some an abhorrent notion and others a cultural asset, describes how zero is misapplied with respect to multiplication and division.

He ends his chapter " A discussion of this rather difficult problem [exactly one number satisfying a definiens] will be omitted here.

To be certain this definition does not lead to a contradiction, it should be preceded by the following theorem: There exists exactly one number x such that, for any number y, one has: Jakub Czajko July " On Cantorian spacetime over number systems with division by zero ", Chaos, Solitons and Fractals , volume 21, number 2, pages — To Continue with Continuity Metaphysica 6, pp.

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