Plus and minus signs
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The plus (+) and minus (-) signs are used universally to represent the operations of addition and subtraction, and have been extended to many other meanings, more or less analogous.
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:
| <hiero>D54- or -D55</hiero> |
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 hüpsche Rechenung auff allen Kauffmanschafft" or Mercantile Arithmetic by Johann Widman 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 (http://members.aol.com/jeff570/operation.html) 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. Recorde wrote, 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.
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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, such as concatenation of strings of characters.
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 string literals is sometimes written: "1"+"1"="11"
Plus and minus signs in other cultures
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 in the 1970s 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" (﬩).
In computing
In Unicode, the plus sign (+) has the code point U+002B.
The minus sign (−) is U+2212. In HTML it can be entered using the character entity − or one of the numeric forms − or −. The Unicode minus sign is designed to be the same length and height as the plus and equals signs. In most fonts these are usually monospaced along with the numbers for ease when being used in tabular formats.
The hyphen-minus sign (-) is U+002D. This 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 should be used for the minus sign only when the character set is limited to ASCII, or with fixed-width fonts.
See also
External links
- The History of Mathematical Symbols - Plus and Minus (http://www.roma.unisa.edu.au/07305/symbols.htm#Plus)
- Earliest uses of various mathematical symbols (http://members.aol.com/jeff570/mathsym.html)fr:Signes plus et moins