The plus and minus signs ( + and −) are mathematical symbols used to represent the notions of positive and negative as well as the operations of addition and subtraction. Their use has been extended to many other meanings, more or less analogous. Plus and minus are Latin terms meaning "more" and "less", respectively.
Nicole Oresme's manuscripts from the 14th century show what may be one of the earliest uses of the plus sign "+". The birth of symbols – Zdena Lustigova, Faculty of Mathematics and Physics Charles University, Prague
In Europe in the early 15th century the letters "P" and "M" were generally used.
The symbols (P with line p̄ for più, i.e., plus, and M with line m̄ for meno, 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 + is a simplification of the Latin "et" (comparable to the ampersand &). The − may be derived from a tilde written over m when used to indicate subtraction; or it may come from a shorthand version of the letter m 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 + ist das mer". They weren't used for addition and subtraction here, but to indicate surplus and deficit; their first use in their modern sense appears in a book by Henricus Grammateus in 1518.
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 have some operation which is called, or is equivalent to, addition. It is conventional to use the plus sign to only denote commutative operations. Moreover, the symbolism has been extended to very different operations; plus can also mean:
All three uses can be referred to as "minus" in everyday speech. In most English-speaking countries, −5 (for example) is normally pronounced "minus five", but in modern US usage it is instead sometimes pronounced "negative five"; here, "minus" may be used by speakers born before 1950, and is still popular in some contexts, but "negative" is usually taught as the only correct reading. Further, some 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.
In some contexts, different glyphs are used for these meanings; for instance in the computer language APL and the expression language used by Texas Instruments graphing calculators (definitely at least the early models including the TI-81 and TI-82) a raised minus sign is used in negative numbers (as in 2 − 5 shows −3), but such usage is uncommon.
In mathematics and most programming languages, the rules for the order of operations mean that −52 is equal to −25: Powers bind more strongly than the unary minus, which binds more strongly than multiplication or division. However, in some programming languages and Microsoft Excel in particular, unary operators bind strongest, so in those cases −5^2 is 25 but 0−5^2 is −25.
Positive and negative are sometimes abbreviated as +ve and −ve.
In mathematics the one-sided limit x→ a+ means x approaches a from the right, and x→ a− means x approaches a from the left. For example, when calculating what x−1 is when x approaches 0, because x−1→+∞ when x→0+ but x−1→−∞ when x→0−.
Blood types are often qualified with a plus or minus to indicate the presence or absence of the Rh factor; for instance, A+ means A-type blood with the Rh factor present, while B− means B-type blood with the Rh factor absent.
In music, augmented chords 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". Also used as superscript.
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 "a" + "b", and results in "ab".
In most programming languages, subtraction and negation are indicated with the ASCII hyphen-minus character, -. In APL a raised minus sign (Unicode U+00AF) is used to denote a negative number, as in ¯3. While in J a negative number is denoted by an underscore, as in _5.
In C and some other computer programming languages, two plus signs indicate the increment operator and two minus signs a decrement. For example, x++ means "increment the value of x by one" and x-- means "decrement the value of x by one". By extension, "++" is sometimes used in computing terminology to signify an improvement, as in the name of the language C++.
In regular expressions, "+" is used to indicate "1 or more" in a pattern to be matched. For example, "x+" means "one or more of the letter x".
There is no concept of negative zero in mathematics, but in computing −0 may have a separate representation from zero. In the IEEE floating-point standard, 1 / −0 is negative infinity (−∞) whereas 1 / 0 is Infinity (∞).
Subscripted plus and minus signs are used as diacritics in the International Phonetic Alphabet 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 (U+02D7) is different from the mathematical minus sign.
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. A double plus (++) is sometimes used to denote double check. Combinations of the plus and minus signs are used to evaluate a move (+/−, +/=, =/+, −/+).
|&minus; &#x2212; &#8722;|
The hyphen-minus sign (-) is the ASCII alternative/version of the minus sign, and doubles as a hyphen. It is usually shorter in length than the plus sign and sometimes at a different height. It can be used as a substitute for the true minus sign when the character set is limited to ASCII. 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.
There is a commercial minus sign (⁒), which looks somewhat like an obelus, at U+2052 (HTML ⁒).
The &#45; entity is HTML 5.