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The plus sign () and the minus sign () are mathematical symbols used to denote positive and negative functions, respectively. In addition, the symbol represents the operation of addition, which results in a sum, while the symbol represents subtraction, resulting in a difference. Their use has been extended to many other meanings, more or less analogous. Plus and minus are Latin terms meaning 'more' and 'less', respectively.
The forms and are used in many countries around the world. Other designs include for plus and for minus.
Nicole Oresme's from the 14th century show what may be one of the earliest uses of as a sign for plus. The birth of symbols – Zdena Lustigova, Faculty of Mathematics and Physics Charles University, Prague
In early 15th century Europe, the letters "P" and "M" were generally used. The symbols (P with overline, , for più (more), i.e., plus, and M with overline, , for meno (less), i.e., minus) appeared for the first time in Luca Pacioli's mathematics compendium, Summa de arithmetica, geometria, proportioni et proportionalità, first printed and published in Venice in 1494.
The sign is a simplification of the (comparable to the evolution of the ampersand ). The may be derived from a macron 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 mehr; "more"): "... was − ist das ist minus ... und das + das ist mer das zu addirst". They were not 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, 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."
The plus sign can also indicate many other operations, depending on the mathematical system under consideration. Many algebraic structures, such as and , 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 and physics. For more, see .
In many contexts, it does not matter whether the second or the third of these usages is intended: −5 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".)Steven Schwartzman (1994). 9780883855119, The Mathematical Association of America. . ISBN 9780883855119 Further, a few textbooks in the United States encourage − x to be read as "the opposite of x" or "the additive inverse of x"—to avoid giving the impression that − x is necessarily negative (since x itself may already be negative).
In mathematics and most programming languages, the rules for the order of operations mean that −52 is equal to −25: Exponentiation binds more strongly than the unary minus, which binds more strongly than multiplication or division. However, in some programming languages (Microsoft Excel 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 and physics. (For more, see below.)
In US grading systems, 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 ).
A common trend in branding, particularly with streaming video services, has been the use of the plus sign at the end of brand names, e.g. Google+, Disney+, Paramount+, and Apple TV+. Since the word "plus" can mean an advantage, or an additional amount of something, such "+" signs imply that a product offers extra features or benefits.
Positive and negative are sometimes abbreviated as and ,. and on batteries and cell terminals are often marked with and .
When placed after special sets of numbers, plus and minus signs are used to indicate that only positive numbers and negative numbers are included, respectively. For example, is the set of all positive and is the set of all negative integers. In these cases, a subscript 0 may also be added to clarify that 0 is included.
Plus and minus signs are often used in tree view on a computer screen—to show if a folder is collapsed or not.
In some programming languages, concatenation of strings is written , and results in .
In most programming languages, subtraction and negation are indicated with the ASCII hyphen-minus character, . In APL a raised minus sign (here written using ) is used to denote a negative number, as in . While in J a negative number is denoted by an underscore, 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++.
In regular expressions, is often used to indicate "1 or more" in a pattern to be matched. For example, means "one or more of the letter x". This is the Kleene plus notation. Hyphen-minus usually indicates a range ( - any capital from 'A' to 'Z'), although it can stand for itself ( any capital from 'A' to 'E' or '-').
There is no concept of negative zero in mathematics, but in computing Signed zero may have a separate representation from zero. In the IEEE floating-point standard, 1 / −0 is negative infinity () whereas 1 / 0 is Infinity ().
is also used to denote added lines in [[|diff]] output in the or the .
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).
A plus sign prefixed to a telephone number is used to indicate the form used for International Direct Dialing. Its precise usage varies by technology and national standards. In the International Phonetic Alphabet, 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 language, Krumen language, Karaboro, Mwan language, Wan language, Yaouré, Wè, Nyabwa language, and Godie language.Hartell, Rhonda L., ed. (1993), The Alphabets of Africa. Dakar: UNESCO and SIL. The Unicode character used for the tone letter () is different from the mathematical minus sign.
The plus sign sometimes represents in the orthography of Huichol.
In the algebraic notation used to record games of chess, the plus sign is used to denote a move that puts the opponent into check, while a double plus is sometimes used to denote double check. Combinations of the plus and minus signs are used to evaluate a move (+/−, +/=, =/+, −/+).
In linguistics, a superscript plus sometimes replaces the asterisk, which denotes unattested linguistic reconstruction.
In , a plus sign denotes graft-chimaera.
In Catholicism, the plus sign before a last name denotes a Bishop, and a double plus is used to denote an Archbishop.
The hyphen-minus symbol () is the form of hyphen most commonly used in digital . On most keyboards, it is the only character that resembles a minus sign or a dash so it is also used for these. The name hyphen-minus derives from the original ASCII standard, where it was called hyphen–(minus). The character is referred to as a hyphen, a minus sign, or a dash according to the context where it is being used.
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