Plus and minus signs

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This article is about mathematical symbols. For the banking network, see PLUS.

For the student loan, see PLUS loan.

The plus and minus signs (+ and −) are 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.

1 History
2 Alternate uses
3 The minus sign
4 Alternative plus sign
5 In computing
6 See also
7 External links

[edit] 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 varying directions), with the reverse sign indicating subtraction:

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.

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.

[edit] Alternate uses

The plus sign can mean many different 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
logical conjunction (usually written ∧): 1+1=1
logical disjunction (usually written ∨): 1+1=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.

[edit] The minus sign

The minus sign has two uses in mathematics:

The subtraction operator: A binary operator to indicate the operation of subtraction, as in 5 − 3 = 2. Subtraction is the opposite of addition.
The negation operator: A unary operator to negate a number, as in −5.

[edit] Alternative plus sign

A Jewish tradition dating at least from the 19th century is to write plus using a symbol like an inverted T. This practice was adopted into Israeli schools (this practice goes back to at least the 1950s) and is now commonplace in most elementary schools (including secular schools) and some secondary schools. It is also used occasionally in books by religious authors, but most books for adults use the international symbol "+". The usual explanation for the practice is that it avoids the writing of a symbol "+" that looks like a Christian cross. Unicode has this symbol at position U+FB29 "Hebrew letter alternative plus sign" (﬩).

[edit] In computing

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.