The plus and minus signs, and , are mathematical symbols used to represent the notions of positive and negative, respectively. In addition, represents the operation of addition, which results in a sum, while represents

=3−2 into Excel or 3−2= into the Windows calculator won't work.
As the true minus is not available on most

"In Israel the plus sign used in mathematics is represented by a horizontal stroke with a vertical hook instead of the sign otherwise used all over the world, because the latter is reminiscent of a cross." (Page 96) It is also used occasionally in books by religious authors, but most books for adults use the international symbol . The reason for this practice is that it avoids the writing of a symbol that looks like a Christian cross.Unicode U+FB29 reference page

This form of the plus sign is also used on the control buttons at individual seats on board the El Al Israel Airlines aircraft.

subtraction
Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign, . For example, in the adjacent picture, there are peaches—meaning 5 peaches with 2 taken ...

, resulting in a difference
Difference, The Difference, Differences or Differently may refer to:
Music
* ''Difference'' (album), by Dreamtale, 2005
* ''Differently'' (album), by Cassie Davis, 2009
** "Differently" (song), by Cassie Davis, 2009
* ''The Difference'' (al ...

. Their use has been extended to many other meanings, more or less analogous. ''Plus'' and ''minus'' are Latin
Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of ...

terms meaning "more" and "less", respectively.
History

Though the signs now seem as familiar as thealphabet
An alphabet is a standardized set of basic written graphemes (called letters) that represent the phonemes of certain spoken languages. Not all writing systems represent language in this way; in a syllabary, each character represents a sylla ...

or the Hindu-Arabic numerals
Arabic numerals are the ten numerical digits: , , , , , , , , and . They are the most commonly used symbols to write decimal numbers. They are also used for writing numbers in other systems such as octal, and for writing identifiers such as ...

, they are not of great antiquity. The Egyptian hieroglyph
Egyptian hieroglyphs (, ) were the formal writing system used in Ancient Egypt, used for writing the Egyptian language. Hieroglyphs combined logographic, syllabic and alphabetic elements, with some 1,000 distinct characters.There were about 1 ...

ic sign for addition, for example, resembled a pair of legs walking in the direction in which the text was written ( Egyptian could be written either from right to left or left to right), with the reverse sign indicating subtraction:
Nicole Oresme's manuscripts
A manuscript (abbreviated MS for singular and MSS for plural) was, traditionally, any document written by hand – or, once practical typewriters became available, typewritten – as opposed to mechanically printed or reproduced in ...

from the 14th century show what may be one of the earliest uses of as a sign for plus.
In early 15th century Europe, the letters "P" and "M" were generally used.
The symbols (P with overline, , for (more), i.e., plus, and M with overline, , for (less), i.e., minus) appeared for the first time in Luca Pacioli
Fra Luca Bartolomeo de Pacioli (sometimes ''Paccioli'' or ''Paciolo''; 1447 – 19 June 1517) was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and an early contributor to the field now known as accounting ...

's mathematics compendium
A compendium (plural: compendia or compendiums) is a comprehensive collection of information and analysis pertaining to a body of knowledge. A compendium may concisely summarize a larger work. In most cases, the body of knowledge will concern a sp ...

, , first printed and published in Venice
Venice ( ; it, Venezia ; vec, Venesia or ) is a city in northeastern Italy and the capital of the Veneto region. It is built on a group of 118 small islands that are separated by canals and linked by over 400 bridges. The is ...

in 1494.
The sign is a simplification of the la, et (comparable to the evolution of the ampersand
The ampersand, also known as the and sign, is the logogram , representing the conjunction "and". It originated as a ligature of the letters ''et''—Latin for "and".
Etymology
Traditionally in English, when spelling aloud, any letter that ...

). The may be derived from a tilde
The tilde () or , is a grapheme with several uses. The name of the character came into English from Spanish, which in turn came from the Latin '' titulus'', meaning "title" or "superscription". Its primary use is as a diacritic (accent) i ...

written over when used to indicate subtraction; or it may come from a shorthand version of the letter itself.
In his 1489 treatise, Johannes Widmann referred to the symbols and as ''minus'' and ''mer'' (Modern German ; "more"): They weren't used for addition and subtraction in the treatise, but were used to indicate surplus and deficit; usage in the modern sense is attested in a 1518 book by Henricus Grammateus.
Robert Recorde, the designer of the equals sign
The equals sign (British English, Unicode) or equal sign (American English), also known as the equality sign, is the mathematical symbol , which is used to indicate equality in some well-defined sense. In an equation, it is placed between two ...

, introduced plus and minus to Britain in 1557 in '' The Whetstone of Witte'': "There be other 2 signes in often use of which the first is made thus + and betokeneth more: the other is thus made − and betokeneth lesse."
Plus sign

The plus sign, , is abinary operator
In mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element. More formally, a binary operation is an operation of arity two.
More specifically, an internal binary op ...

that indicates addition, as in . It can also serve as a unary operator that leaves its operand
In mathematics, an operand is the object of a mathematical operation, i.e., it is the object or quantity that is operated on.
Example
The following arithmetic expression shows an example of operators and operands:
:3 + 6 = 9
In the above exampl ...

unchanged ( means the same as ). This notation may be used when it is desired to emphasize the positiveness of a number, especially in contrast with the negative number
In mathematics, a negative number represents an opposite. In the real number system, a negative number is a number that is less than zero. Negative numbers are often used to represent the magnitude of a loss or deficiency. A debt that is owed m ...

s ( versus ).
The plus sign can also indicate many other operations, depending on the mathematical system under consideration. Many algebraic structure
In mathematics, an algebraic structure consists of a nonempty set ''A'' (called the underlying set, carrier set or domain), a collection of operations on ''A'' (typically binary operations such as addition and multiplication), and a finite set o ...

s, such as vector space
In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called ''vectors'', may be added together and multiplied ("scaled") by numbers called '' scalars''. Scalars are often real numbers, but ca ...

s and matrix ring
In abstract algebra, a matrix ring is a set of matrices with entries in a ring ''R'' that form a ring under matrix addition and matrix multiplication . The set of all matrices with entries in ''R'' is a matrix ring denoted M''n''(''R'')Lang, ...

s, have some operation which is called, or is equivalent to, addition. It is though conventional to use the plus sign to only denote commutative operations.
The symbol is also used in chemistry
Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, propertie ...

and physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which rel ...

. For more, see .
Minus sign

The minus sign, , has three main uses in mathematics: # Thesubtraction
Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign, . For example, in the adjacent picture, there are peaches—meaning 5 peaches with 2 taken ...

operator: a binary operator
In mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element. More formally, a binary operation is an operation of arity two.
More specifically, an internal binary op ...

to indicate the operation of subtraction, as in 5 − 3 = 2. Subtraction is the inverse of addition.
# The function
Function or functionality may refer to:
Computing
* Function key, a type of key on computer keyboards
* Function model, a structured representation of processes in a system
* Function object or functor or functionoid, a concept of object-orient ...

whose value for any real or complex
Complex commonly refers to:
* Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe
** Complex system, a system composed of many components which may interact with each ...

argument
An argument is a statement or group of statements called premises intended to determine the degree of truth or acceptability of another statement called conclusion. Arguments can be studied from three main perspectives: the logical, the dialect ...

is the additive inverse of that argument. For example, if , then , but if , then . Similarly, .
# A prefix
A prefix is an affix which is placed before the stem of a word. Adding it to the beginning of one word changes it into another word. For example, when the prefix ''un-'' is added to the word ''happy'', it creates the word ''unhappy''. Particul ...

of a numeric constant. When it is placed immediately before an unsigned numeral, the combination names a negative number, the additive inverse of the positive number that the numeral would otherwise name. In this usage, '' names a number the same way 'semicircle' names a geometric figure, with the caveat that 'semi' does not have a separate use as a function name.
In many contexts, it does not matter whether the second or the third of these usages is intended: is the same number. When it is important to distinguish them, a raised minus sign is sometimes used for negative constants, as in elementary education, the programming language APL, and some early graphing calculators.
All three uses can be referred to as "minus" in everyday speech, though the binary operator is sometimes read as "take away". In American English nowadays, −5 (for example) is generally referred to as "negative five" though speakers born before 1950 often refer to it as "minus five". (Temperatures tend to follow the older usage; −5° is generally called "minus five degrees".) Further, a few textbooks in the United States encourage to be read as "the opposite of " or "the additive inverse of "—to avoid giving the impression that is necessarily negative (since itself may already be negative).
In mathematics and most programming languages, the rules for the order of operations
In mathematics and computer programming, the order of operations (or operator precedence) is a collection of rules that reflect conventions about which procedures to perform first in order to evaluate a given mathematical expression.
For exampl ...

mean that is equal to : Exponentiation
Exponentiation is a mathematical operation, written as , involving two numbers, the '' base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to r ...

binds more strongly than the unary minus, which binds more strongly than multiplication or division. However, in some programming languages (Microsoft Excel
Microsoft Excel is a spreadsheet developed by Microsoft for Microsoft Windows, Windows, macOS, Android (operating system), Android and iOS. It features calculation or computation capabilities, graphing tools, pivot tables, and a macro (comp ...

in particular), unary operators bind strongest, so in those cases is 25, but is −25.
Similar to the plus sign, the minus sign is also used in chemistry
Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, propertie ...

and physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which rel ...

. For more, see below.
Use in elementary education

Some elementary teachers use raised plus and minus signs before numbers to show they are positive or negative numbers. For example, subtracting −5 from 3 might be read as "positive three take away negative 5", and be shown as : becomes , or even as : becomes .Use as a qualifier

In grading systems (such as examination marks), the plus sign indicates a grade one level higher and the minus sign a grade lower. For example, ("B minus") is one grade lower than . In some occasions, this is extended to two plus or minus signs (e.g., being two grades higher than ). Positive and negative are sometimes abbreviated as and .Mathematics

In mathematics the one-sided limit means approaches from the right (i.e., right-sided limit), and means approaches from the left (i.e., left-sided limit). For example, as but as .Blood

Blood types
Blood is a body fluid in the circulatory system of humans and other vertebrates that delivers necessary substances such as nutrients and oxygen to the cells, and transports metabolic waste products away from those same cells. Blood in the ci ...

are often qualified with a plus or minus to indicate the presence or absence of the Rh factor
The Rh blood group system is a human blood group system. It contains proteins on the surface of red blood cells. After the ABO blood group system, it is the most likely to be involved in transfusion reactions. The Rh blood group system consists ...

. For example, A+ means type A blood with the Rh factor present, while B− means type B blood with the Rh factor absent.
Music

In music,augmented chord
Augment or augmentation may refer to:
Language
* Augment (Indo-European), a syllable added to the beginning of the word in certain Indo-European languages
* Augment (Bantu languages), a morpheme that is prefixed to the noun class prefix of nouns ...

s are symbolized with a plus sign, although this practice is not universal (as there are other methods for spelling those chords). For example, "C+" is read "C augmented chord". Sometimes the plus is written as a superscript.
Uses in computing

As well as the normal mathematical usage, plus and minus signs may be used for a number of other purposes in computing. Plus and minus signs are often used intree view
In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, including only woody plants with secondary growth, plants that are ...

on a computer screen—to show if a folder is collapsed or not.
In some programming languages, concatenation
In formal language theory and computer programming, string concatenation is the operation of joining character strings end-to-end. For example, the concatenation of "snow" and "ball" is "snowball". In certain formalisations of concatenat ...

of string
String or strings may refer to:
* String (structure), a long flexible structure made from threads twisted together, which is used to tie, bind, or hang other objects
Arts, entertainment, and media Films
* ''Strings'' (1991 film), a Canadian ani ...

s is written , and results in .
In most programming languages, subtraction and negation are indicated with the ASCII hyphen-minus
The hyphen-minus is the most commonly used type of hyphen, widely used in digital documents. It is the only character that looks like a minus sign or a dash in many character sets such as ASCII or on most keyboards, so it is also used as such ...

character, . In APL a raised minus sign (Unicode U+00AF) is used to denote a negative number, as in . While in J a negative number is denoted by an underscore
An underscore, ; also called an underline, low line, or low dash; is a line drawn under a segment of text. In proofreading, underscoring is a convention that says "set this text in italic type", traditionally used on manuscript or typescript as ...

, as in .
In C and some other computer programming languages, two plus signs indicate the increment operator and two minus signs a decrement; the position of the operator before or after the variable indicates whether the new or old value is read from it. For example, if x equals 6, then increments x to 7 but sets y to 6, whereas would set both x and y to 7. By extension, is sometimes used in computing terminology to signify an improvement, as in the name of the language C++
C++ (pronounced "C plus plus") is a high-level general-purpose programming language created by Danish computer scientist Bjarne Stroustrup as an extension of the C programming language, or "C with Classes". The language has expanded signific ...

.
In regular expression
A regular expression (shortened as regex or regexp; sometimes referred to as rational expression) is a sequence of characters that specifies a search pattern in text. Usually such patterns are used by string-searching algorithms for "find" ...

s, is often used to indicate "1 or more" in a pattern to be matched. For example, means "one or more of the letter x".
There is no concept of negative zero in mathematics, but in computing −0
Signed zero is zero with an associated sign. In ordinary arithmetic, the number 0 does not have a sign, so that −0, +0 and 0 are identical. However, in computing, some number representations allow for the existence of two zeros, often denoted by ...

may have a separate representation from zero. In the IEEE floating-point standard, 1 / −0 is negative infinity ($-\backslash infty$) whereas 1 / 0 is positive infinity ( $\backslash infty$).
Other uses

In physics, the use of plus and minus signs for differentelectrical charge
Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described ...

s was introduced by Georg Christoph Lichtenberg.
In chemistry, superscripted plus and minus signs are used to indicate an ion with a positive or negative charge of 1 (e.g., NH). If the charge is greater than 1, a number indicating the charge is written before the sign (as in SO). The minus sign is also used, in place of an en dash
The dash is a punctuation mark consisting of a long horizontal line. It is similar in appearance to the hyphen but is longer and sometimes higher from the baseline. The most common versions are the endash , generally longer than the hyphen b ...

, for a single covalent bond between two atoms as in the skeletal formula
The skeletal formula, or line-angle formula or shorthand formula, of an organic compound is a type of molecular structural formula that serves as a shorthand representation of a molecule's bonding and some details of its molecular geometry. A ...

.
In the International Phonetic Alphabet
The International Phonetic Alphabet (IPA) is an alphabetic system of phonetic notation based primarily on the Latin script. It was devised by the International Phonetic Association in the late 19th century as a standardized representation o ...

, subscript
A subscript or superscript is a character (such as a number or letter) that is set slightly below or above the normal line of type, respectively. It is usually smaller than the rest of the text. Subscripts appear at or below the baseline, while ...

ed plus and minus signs are used as diacritics to indicate advanced or retracted articulations of speech sounds.
The minus sign is also used as tone letter in the orthographies of Dan, Krumen, Karaboro
The Karaboro languages are spoken in Burkina Faso by approximately 65,000 people (SIL 1995/1991). They belong to the Senufo subfamily, but are separated from other Senufo languages by a small band of unrelated languages. Within Senufo they are th ...

, Mwan, Wan, Yaouré, Wè, Nyabwa and Godié. The Unicode character used for the tone letter (U+02D7) is different from the mathematical minus sign.
The plus sign sometimes represents in the orthography of Huichol
The Huichol or Wixárika are an indigenous people of Mexico and the United States living in the Sierra Madre Occidental range in the states of Nayarit, Jalisco, Zacatecas, and Durango, as well as in the United States in the states of Californi ...

.
In the algebraic notation used to record games of chess
Chess is a board game for two players, called White and Black, each controlling an army of chess pieces in their color, with the objective to checkmate the opponent's king. It is sometimes called international chess or Western chess to dis ...

, the plus sign is used to denote a move that puts the opponent into check
Check or cheque, may refer to:
Places
* Check, Virginia
Arts, entertainment, and media
* ''Check'' (film), a 2021 Indian Telugu-language film
* ''The Checks'' (episode), a 1996 TV episode of ''Seinfeld''
Games and sports
* Check (chess), a t ...

, while a double plus is sometimes used to denote double check
In chess and other related games, a double check is a check delivered by two pieces simultaneously. In chess notation, it is almost always represented the same way as a single check ("+"), but it is sometimes symbolized by "++" (however, "++" is ...

. Combinations of the plus and minus signs are used to evaluate a move (+/−, +/=, =/+, −/+).
In linguistics, a superscript plus sometimes replaces the asterisk
The asterisk ( ), from Late Latin , from Ancient Greek , ''asteriskos'', "little star", is a typographical symbol. It is so called because it resembles a conventional image of a heraldic star.
Computer scientists and mathematicians often vo ...

, which denotes unattested linguistic reconstruction
Linguistic reconstruction is the practice of establishing the features of an unattested ancestor language of one or more given languages. There are two kinds of reconstruction:
* Internal reconstruction uses irregularities in a single language t ...

.
In botanical name
A botanical name is a formal scientific name conforming to the '' International Code of Nomenclature for algae, fungi, and plants'' (ICN) and, if it concerns a plant cultigen, the additional cultivar or Group epithets must conform to the ''Intern ...

s, a plus sign denotes graft-chimaera
In horticulture, a graft-chimaera may arise in grafting at the point of contact between rootstock and scion and will have properties intermediate between those of its "parents". A graft-chimaera is not a true hybrid but a mixture of cells, each ...

.
A plus sign written at the beginning of an international phone number is the " international prefix symbol" that "serves to remind the subscriber to dial the international prefix which differs from country to country and also serves to identify the number following as the international telephone number."
Character codes

The hyphen-minus sign, , is the originalASCII
ASCII ( ), abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices. Because of ...

version of the minus sign, which doubles as a hyphen
The hyphen is a punctuation mark used to join words and to separate syllables of a single word. The use of hyphens is called hyphenation. ''Son-in-law'' is an example of a hyphenated word. The hyphen is sometimes confused with dashes ( figur ...

. It is usually shorter in length than the plus sign and often at a different height to the plus-sign's cross bar. It can be used as a substitute for the true minus sign when the character set is limited to ASCII
ASCII ( ), abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices. Because of ...

. Most programming languages and other computer readable languages do this, since ASCII is generally available as a subset of most character encodings, while U+2212 is a Unicode feature only. Also several other software programs usable for calculations don't accept the U+2212 minus. For example, pasting keyboard layout
A keyboard layout is any specific physical, visual or functional arrangement of the keys, legends, or key-meaning associations (respectively) of a computer keyboard, mobile phone, or other computer-controlled typographic keyboard.
is the actua ...

s, typographers sometimes use the very similar en dash
The dash is a punctuation mark consisting of a long horizontal line. It is similar in appearance to the hyphen but is longer and sometimes higher from the baseline. The most common versions are the endash , generally longer than the hyphen b ...

, U+2013, to represent the minus sign although it is "not preferred" in mathematical typesetting. Ways of producing the en dash are available on most computers; see .
Alternative minus signs

There is a commercial minus sign, , which is used in Germany and Scandinavia. The symbol is used to denote subtraction inScandinavia
Scandinavia; Sámi languages: /. ( ) is a subregion in Northern Europe, with strong historical, cultural, and linguistic ties between its constituent peoples. In English usage, ''Scandinavia'' most commonly refers to Denmark, Norway, and Swe ...

.
Alternative plus sign

A Jewish tradition that dates from at least the 19th century is to write ''plus'' using the symbol . This practice was adopted intoIsrael
Israel (; he, יִשְׂרָאֵל, ; ar, إِسْرَائِيل, ), officially the State of Israel ( he, מְדִינַת יִשְׂרָאֵל, label=none, translit=Medīnat Yīsrāʾēl; ), is a country in Western Asia. It is situated ...

i schools and is still commonplace today in elementary school
A primary school (in Ireland, the United Kingdom, Australia, Trinidad and Tobago, Jamaica, and South Africa), junior school (in Australia), elementary school or grade school (in North America and the Philippines) is a school for primary ed ...

s (including secular
Secularity, also the secular or secularness (from Latin ''saeculum'', "worldly" or "of a generation"), is the state of being unrelated or neutral in regards to religion. Anything that does not have an explicit reference to religion, either negativ ...

schools) but in fewer secondary school
A secondary school describes an institution that provides secondary education and also usually includes the building where this takes place. Some secondary schools provide both '' lower secondary education'' (ages 11 to 14) and ''upper seconda ...

s.Christian-Jewish Dialogue: Theological Foundations By Peter von der Osten-Sacken (1986 – Fortress Press)"In Israel the plus sign used in mathematics is represented by a horizontal stroke with a vertical hook instead of the sign otherwise used all over the world, because the latter is reminiscent of a cross." (Page 96) It is also used occasionally in books by religious authors, but most books for adults use the international symbol . The reason for this practice is that it avoids the writing of a symbol that looks like a Christian cross.

Unicode
Unicode, formally The Unicode Standard,The formal version reference is is an information technology standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems. The standard, w ...

has this symbol at position .This form of the plus sign is also used on the control buttons at individual seats on board the El Al Israel Airlines aircraft.

See also

*En dash
The dash is a punctuation mark consisting of a long horizontal line. It is similar in appearance to the hyphen but is longer and sometimes higher from the baseline. The most common versions are the endash , generally longer than the hyphen b ...

, a dash that looks similar to the subtraction symbol but is used for different purposes
* Plus–minus sign
The plus–minus sign, , is a mathematical symbol with multiple meanings.
*In mathematics, it generally indicates a choice of exactly two possible values, one of which is obtained through addition and the other through subtraction.
*In experime ...

±
* Glossary of mathematical symbols
* ⊕ (disambiguation)
References and footnotes

External links

* * {{DEFAULTSORT:Plus and minus signs Elementary arithmetic Mathematical symbols Addition Subtraction de:Vorzeichen (Zahl)#Plus- und Minuszeichen