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0 (zero) is a number representing an empty quantity. Adding 0 to any number leaves that number unchanged. In mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and complex numbers, as well as other algebraic structures. Multiplying any number by 0 has the result 0, and consequently, division by zero has no meaning in arithmetic.

Common names for the number 0 in English include zero, nought, naught (/nt/), and nil. In contexts where at least one adjacent digit distinguishes it from the letter O, the number is sometimes pronounced as oh or o (/o/). Informal or slang terms for 0 include zilch and zip. Historically, ought, aught (/t/), and cipher have also been used.

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The word zero came into the English language via French zro from the Italian zero, a contraction of the Venetian zevero form of Italian zefiro via afira or ifr.[1] In pre-Islamic time the word ifr (Arabic ) had the meaning "empty".[2] Sifr evolved to mean zero when it was used to translate nya (Sanskrit: ) from India.[2] The first known English use of zero was in 1598.[3]

Depending on the context, there may be different words used for the number zero, or the concept of zero. For the simple notion of lacking, the words "nothing" and "none" are often used. Sometimes, the word "nought" or "naught" is used.[citation needed]

Ancient Egyptian numerals were of base 10.[6] They used hieroglyphs for the digits and were not positional. In one papyrus written around 1770 BC, a scribe recorded daily incomes and expenditures for the pharaoh's court, using the nfr hieroglyph to indicate cases where the amount of a foodstuff received was exactly equal to the amount disbursed. Egyptologist Alan Gardiner suggested that the nfr hieroglyph was being used as a symbol for zero. The same symbol 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.[7]

By the middle of the 2nd millennium BC, Babylonian mathematics had a sophisticated base 60 positional numeral system. The lack of a positional value (or zero) was indicated by a space between sexagesimal numerals. In a tablet unearthed at Kish (dating to as early as 700 BC), the scribe Bl-bn-aplu used three hooks as a placeholder in the same Babylonian system.[8] By 300 BC, a punctuation symbol (two slanted wedges) was repurposed as a placeholder.[9][10]

The Mesoamerican Long Count calendar developed in south-central Mexico and Central America required the use of zero as a placeholder within its vigesimal (base-20) positional numeral system. Many different glyphs, including the partial quatrefoil were used as a zero symbol for these Long Count dates, the earliest of which (on Stela 2 at Chiapa de Corzo, Chiapas) has a date of 36 BC.[a][citation needed]

Since the eight earliest Long Count dates appear outside the Maya homeland,[12] it is generally believed that the use of zero in the Americas predated the Maya and was possibly the invention of the Olmecs.[13] Many of the earliest Long Count dates were found within the Olmec heartland, although the Olmec civilization ended by the 4th century BC, several centuries before the earliest known Long Count dates.[citation needed]

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 not to have influenced Old World numeral systems.[citation needed]

The ancient Greeks had no symbol for zero (, pronounced 'midn'), and did not use a digit placeholder for it.[14] According to mathematician Charles Seife, the ancient Greeks did begin to adopt the Babylonian placeholder zero for their work in astronomy after 500 BC, representing it with the lowercase Greek letter tag_hash_133 (tag_hash_134: omicron). However, after using the Babylonian placeholder zero for astronomical calculations they would typically convert the numbers back into Greek numerals. Greeks seemed to have a philosophical opposition to using zero as a number.[15] Other scholars give the Greek partial adoption of the Babylonian zero a later date, with neuroscientist Andreas Nieder giving a date of after 400 BC and mathematician Robert Kaplan dating it after the conquests of Alexander.[16][17]

Greeks seemed unsure about the status of zero as a number. Some of them asked themselves, "How can not being be?", 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.[18]

The Lokavibhga, a Jain text on cosmology surviving in a medieval Sanskrit translation of the Prakrit original, which is internally dated to AD 458 (Saka era 380), uses a decimal place-value system, including a zero. In this text, nya ("void, empty") is also used to refer to zero.[42]

Rules governing the use of zero appeared in Brahmagupta's Brahmasputha Siddhanta (7th century), which states the sum of zero with itself as zero, and incorrectly describes division by zero in the following way:[46][47]

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.

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 Chaturbhuj Temple, Gwalior, in India, dated 876.[49][50]

In AD 813, astronomical tables were prepared by a Persian mathematician, Muammad ibn Ms al-Khwrizm, using Hindu numerals;[52] and about 825, he published a book synthesizing Greek and Hindu knowledge and also contained his own contribution to mathematics including an explanation of the use of zero.[53] This book was later translated into Latin in the 12th century under the title Algoritmi de numero Indorum. 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 to acquire a meaning of any arithmetic based on decimals.[52]

The concept of zero plays multiple roles in mathematics: as a digit, it is an important part of positional notation for representing numbers, while it also plays an important role as a number in its own right in many algebraic settings.

The role of 0 as additive identity generalizes beyond elementary algebra. In abstract algebra, 0 is commonly used to denote a zero element, which is the identity element for addition (if defined on the structure under consideration) and an absorbing element for multiplication (if defined). (Such elements may also be called zero elements.) Examples include identity elements of additive groups and vector spaces. Another example is the zero function (or zero map) on a domain D. This is the constant function with 0 as its only possible output value, that is, it is the function f defined by f(x) = 0 for all x in D. As a function from the real numbers to the real numbers, the zero function is the only function that is both even and odd.

In databases, it is possible for a field not to have a value. It is then said to have a null value.[79] 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.[80]

An epoch, in computing terminology, is the date and time associated with a zero timestamp. The Unix epoch begins the midnight before the first of January 1970.[81][82][83] The Classic Mac OS epoch and Palm OS epoch begin the midnight before the first of January 1904.[84]

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.[citation needed]

In comparative zoology and cognitive science, recognition that some animals display awareness of the concept of zero leads to the conclusion that the capability for numerical abstraction arose early in the evolution of species.[86]

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The growth in net-zero pledges has been accompanied by a proliferation of criteria with varying levels of robustness. To develop stronger and clearer standards for net-zero emissions pledges by non-State entities such as businesses, investors, cities and regions, and speed up their implementation, UN Secretary-General Antnio Guterres in March 2022 established a High-Level Expert Group on the Net-Zero Emissions Commitments of Non-State Entities. The Expert Group presented its recommendations at COP27 on 8 November 2022.

Governments have the biggest responsibility in the transition to net-zero emissions by mid-century. But businesses, investors, cities, states and regions also needs to live up to their net-zero promises. A high-level expert group convened by the UN Secretary-General and chaired by former Canadian Minister Catherine McKenna developed stronger and clearer standards for net-zero emissions pledges by non-State entities. Learn more e24fc04721