Plus and minus signs

[4][5] The symbols (P with overline, p̄, for più (more), i.e., plus, and M with overline, m̄, 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.

[7] The − may be derived from a macron ◌̄ written over ⟨m⟩ when used to indicate subtraction; or it may come from a shorthand version of the letter ⟨m⟩ itself.

[9][10][11] 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.

Many algebraic structures, such as vector spaces and matrix rings, have some operation which is called, or is equivalent to, addition.

The minus sign (−) has three main uses in mathematics:[16] 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.

(Temperatures tend to follow the older usage; −5° is generally called "minus five degrees".

However, in some programming languages (Microsoft Excel in particular), unary operators bind strongest, so in those cases −5^2 is 25, but 0−5^2 is −25.

Some elementary teachers use raised minus signs before numbers to disambiguate them from the operation of subtraction.

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.

Blood types are often qualified with a plus or minus to indicate the presence or absence of the Rh factor.

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 in tree view on a computer screen—to show if a folder is collapsed or not.

In most programming languages, subtraction and negation are indicated with the ASCII hyphen-minus character, -.

In APL a raised minus sign (here written using U+00AF ¯ MACRON) is used to denote a negative number, as in ¯3.

In physics, the use of plus and minus signs for different electrical charges 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+4 ).

A plus sign prefixed to a telephone number is used to indicate the form used for International Direct Dialing.

In the International Phonetic Alphabet, subscripted 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, Mwan, Wan, Yaouré, Wè, Nyabwa, and Godié.

Variants of the symbols have unique codepoints in Unicode: There is a commercial minus sign, ⁒, which is used in Germany and Scandinavia.

[27] The name hyphen-minus derives from the original ASCII standard,[28] where it was called hyphen–(minus).