Plus and minus signs

؋ ​₳ ​฿ ​₿ ​₵ ​¢ ​₡ ​₢ ​$ ​₫ ​₯ ​֏ ​₠ ​€ ​ƒ ​₣ ​₲ ​₴ ​₭ ​₺ ​₾ ​₼ ​ℳ ​₥ ​₦ ​₧ ​₱ ​₰ ​£ ​元 圆 圓 ​﷼ ​៛ ​₽ ​₹ ₨ ​₪ ​৳ ​₸ ​₮ ​₩ ​¥ ​円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. 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. 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 could be written either from right to left or left to right), with the reverse sign indicating subtraction: Nicole Oresme's manuscripts from the 14th century show what may be one of the earliest uses of the plus sign '+'. 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 (+) 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 (+x means the same as x). This notation may be used when it is desired to emphasize 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 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: The minus sign (−) has three main uses in mathematics: In many contexts, it does not matter whether the second or the third of these usages is intended. −5 is the same number either way. Sometimes, it does make a difference꞉ the programming language APL uses the special character ¯ (Unicode U+00AF) for this purpose so that the interpreter of APL has less work when taking ¯5 as the number −5 rather than inverting the constant 5 by means of the function − above. As described in the next section, some educators consider it important that elementary students realize that negative numbers are genuine entities that can be given names and so use a raised minus in the name of a negative number. Similarly, in 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).