Plus and minus signs
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, with the reverse sign indicating subtraction:Nicole Oresme's manuscripts from the 14th century show what may be one of the earliest uses of as a sign for plus.
In Europe in the early 15th century the letters "P" and "M" were generally used.
The symbols, i.e., plus, and M with overline,, for meno appeared for the first time in Luca Pacioli’s mathematics compendium, Summa de arithmetica, first printed and published in Venice in 1494. The is a simplification of the Latin et. The may be derived from a tilde written over when used to indicate subtraction; or it may come from a shorthand version of the letter itself. In his 1489 treatise Johannes Widmann referred to the symbols and as minus and mer : "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."
Plus sign
The plus sign,, is a binary operator that indicates addition, as in. It can also serve as a unary operator that leaves its operand unchanged. This notation may be used when it is desired to emphasize the positiveness of a number, especially when contrasting with the negative.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.
The symbol is also used in chemistry and physics, see below.
Minus sign
The minus sign,, has three main uses in mathematics:- The subtraction operator: a binary operator to indicate the operation of subtraction, as in 5 − 3 = 2. Subtraction is the inverse of addition.
- The function whose value for any real or complex argument is the additive inverse of that argument. For example, if, then, but if, then. Similarly,.
- A prefix of a numeric constant. When it is placed immediately before an unsigned numeral, the combination names a negative number, the additive inverse of the positive number that the numeral would otherwise name. In this usage, names a number just as 'semicircle' names a geometric figure, the difference being that 'semi' does not have a separate use as a function name.
All three uses can be referred to as "minus" in everyday speech, though the binary operator is sometimes read as "take away". In most English-speaking countries, is normally referred to as "minus five", but in modern US usage it is instead usually called "negative five"; here, "minus" may be used by speakers born before 1950, and is still popular in some contexts, but "negative" is usually taught as the only correct reading. Further, a few textbooks in the United States encourage to be read as "the opposite of " or "the additive inverse of " to avoid giving the impression that is necessarily negative
In mathematics and most programming languages, the rules for the order of operations mean that is equal to : Exponentiation binds more strongly than the unary minus, which binds more strongly than multiplication or division. However, in some programming languages and in Microsoft Excel in particular, unary operators bind strongest, so in those cases is 25 but is −25.
Again, the symbol is also used in chemistry and physics; see below.
Use in elementary education
Some elementary teachers use raised plus and minus signs before numbers to show they are positive or negative numbers. For example, subtracting −5 from 3 might be read as "positive three take away negative 5" and be shown asor even as
Use as a qualifier
In grading systems, the plus sign indicates a grade one level higher and the minus sign a grade lower. For example, is one grade lower than. Sometimes this is extended to two plus or minus signs; for example is two grades higher than.Positive and negative are sometimes abbreviated as and.
Mathematics
In mathematics the one-sided limit means approaches from the right, and means approaches from the left. For example, as but as.Blood
are often qualified with a plus or minus to indicate the presence or absence of the Rh factor; for instance, A+ means A-type blood with the Rh factor present, while B− means B-type blood with the Rh factor absent.Music
In music, augmented chords are symbolized with a plus sign, although this practice is not universal as there are other methods for spelling those chords. For example, "C+" is read "C augmented chord". Also used as superscript.Uses in computing
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 some programming languages, concatenation of strings is written, and results in.
In most programming languages, subtraction and negation are indicated with the ASCII hyphen-minus character,. In APL a raised minus sign is used to denote a negative number, as in. While in J a negative number is denoted by an underscore, as in.
In C and some other computer programming languages, two plus signs indicate the increment operator and two minus signs a decrement; the position of the operator before or after the variable indicates whether the new or old value is read from it. For example, if x equals 6, then increments x to 7 but sets y to 6, whereas would set both x and y to 7. By extension, is sometimes used in computing terminology to signify an improvement, as in the name of the language C++.
In regular expressions, is often used to indicate "1 or more" in a pattern to be matched. For example, means "one or more of the letter x".
There is no concept of negative zero in mathematics, but in computing −0 may have a separate representation from zero. In the IEEE floating-point standard, 1 / −0 is negative infinity whereas 1 / 0 is positive infinity.
Other uses
In chemistry, superscripted plus and minus signs are used to indicate an ion with a positive or negative charge of 1. If the charge is greater than 1, a number indicating the charge is written before the sign. The minus sign is also used for a single covalent bond between two atoms, as in the skeletal formula. For example, Sulfuric Acid: +In physics, the use of plus and minus signs for different electrical charges was introduced by Georg Christoph Lichtenberg.
Subscripted plus and minus signs are used as diacritics in the International Phonetic Alphabet 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. The Unicode character used for the tone letter is different from the mathematical minus sign.
In the algebraic notation used to record games of chess, the plus sign is used to denote a move that puts the opponent into check. A double plus is sometimes used to denote double check. Combinations of the plus and minus signs are used to evaluate a move.
Character codes
| Read | Character | Unicode | ASCII | in URL | HTML notations |
| Plus | U+002B | + | %2B | + | |
| Minus | U+2212 | %E2%88%92 | − − − | ||
| Hyphen-minus | U+002D | - | %2D | ||
| Small Hyphen-minus | U+FE63 | %EF%B9%A3 | ﹣ ﹣ | ||
| Full-width Plus | U+FF0B | %EF%BC%8B | ＋ ＋ | ||
| Full-width Hyphen-minus | U+FF0D | %EF%BC%8D | － － |
The hyphen-minus sign,, is the original ASCII version of the minus sign, which doubles as a hyphen. It is usually shorter in length than the plus sign and often at a different height to the plus-sign's cross bar. It can be used as a substitute for the true minus sign when the character set is limited to ASCII. Most programming languages and other computer readable languages do this, since ASCII is generally available as a subset of most character encodings, while U+2212 is a Unicode feature only. Also several other softwares usable for calculations don't accept the U+2212 minus. For example pasting
There is a commercial minus sign,, which is used in Germany and Poland. The division sign,, is used to denote subtraction in Norway.
Alternative plus sign
A Jewish tradition that dates from at least the 19th century is to write plus using the symbol. This practice was adopted into Israeli schools and is still commonplace today in elementary schools but in fewer secondary schools. It is also used occasionally in books by religious authors, but most books for adults use the international symbol. The reason for this practice is that it avoids the writing of a symbol that looks like a Christian cross. Unicode has this symbol at position.