Plus and minus signs

This article is about mathematical symbols. For other uses, see Plus (disambiguation). For the record label see Minus (record label) and the comic Minus (comic).

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.

+ –

History

Though the signs now seem as familiar as the alphabet or the Hindu-Arabic numerals, they are not of great antiquity. The Egyptian hieroglyphic sign for addition, for example, resembled a pair of legs walking in the direction in which the text was written (Egyptian was written in boustrophedon, or alternating directions), with the reverse sign indicating subtraction:

or

In Europe in the early 15th century the letters P and M were generally used.

The earliest print appearance of the modern signs seems to come from a book on "Behende und hüpscheenung auff allen Kauffmanschafft" or Mercantile Arithmetic by Johannes Widmann in 1489, used to indicate surpluses and deficits. 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. Widmann referred to the symbols - and + as minus and mer: "was - ist, das ist minus, und das + ist das mer".

According to the Earliest Uses of Various Mathematical Symbols website, a book published by Henricus Grammateus in 1518 is the earliest found to use + and − for addition and subtraction.

Robert Recorde, the designer of the equals sign, introduced plus and minus to the UK 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 a binary operator that indicates addition, as in 2 + 3 = 5. It can also serve as a unary operator that leaves its operand unchanged (+5 means the same as 5). This notation may be used when it is desired to emphasise the positiveness of a number, especially when contrasting with the negative (+5 versus −5).

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 equivalent to, addition. Moreover, the symbolism has been extended to very different operations. Plus can mean:

• exclusive or (usually written ⊕): 1 + 1 = 0, 1 + 0 = 1
• logical disjunction (usually written ∨): 1 + 1 = 1, 1 + 0 = 1
• concatenation of strings is sometimes written: "a" + "b" = "ab", although this usage is questioned by some for violating commutativity, a property addition is expected to have.

In grading systems (such as examination marks), the plus sign indicates a grade one level higher; for example, B+ ("B plus") is one grade higher than B. Sometimes this is extended to two plus signs; for example B++ is one grade higher than B+.

In C and some other computer programming languages, two plus signs indicate the increment operator; for example, x++ means "increment 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++.

Plus and minus signs are often used in tree view on a computer screen to show if a folder is collapsed or not.

Minus sign

The minus sign has two uses in mathematics:

1. The subtraction operator: A binary operator to indicate the operation of subtraction, as in 5 − 3 = 2. Subtraction is the inverse of addition.
2. A unary operator that acts as an instruction to replace the operand by its negative (or "opposite"). When applied to a positive number, unary minus creates a negative number. For example, −5 is the negative of 5, and −10.4 is the negative of 10.4. When applied to a negative number unary minus creates a positive number (the opposite of a negative is a positive). For example, if x is 3, then −x is −3, but if x is −3, then −x is 3. Similarly, −(−2) is equal to 2. When applied to zero the result is zero (−0 = 0).

Technically, only the first use should be read minus. The number −5 should be read "negative 5" and the symbol −x should be read "the opposite of x". In practice, however, almost everyone says "minus five" and "minus x".

In some contexts, different glyphs are used for these meanings; e.g., the unary operator may be raised (as in 2 – 5 = ¯3), but this usage is rare.

In grading systems (such as examination marks), the minus sign indicates a grade one level lower; for example, B− ("B minus") is one grade lower than B. Sometimes this is extended to two minus signs; for example B−− is one grade lower than B−.

In C and some other computer programming languages, two minus signs indicate the decrement operator; for example, x−− means "decrement the value of x by one".

Character codes

Read	Character	Unicode	ASCII	URL	HTML (others)
Plus	+	U+002B	+	%2b
Minus	−	U+2212			− or −
Hyphen-minus	-	U+002d	-	%2d

The Unicode minus sign is designed to be the same length and height as the plus and equals signs. In most fonts these are the same width as digits in order to facilitate the alignment of numbers in tables.

The hyphen-minus sign (-) is the ASCII 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.

See also

• Plus-minus sign
• Table of mathematical symbols
• Graft-chimaera for the meaning of + in botanical names
• Dash

External links

• The History of Mathematical Symbols - Plus and Minus
• Earliest uses of various mathematical symbols