Plus and minus signs

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See also Subtraction, Minus (disambiguation), Positive sign (astrology), Negative sign (astrology), or Plus-minus (disambiguation). Plus and minus signs_sentence_0

For the symbol "±", see Plus-minus sign. Plus and minus signs_sentence_1

Plus and minus signs_table_infobox_0

+  −Plus and minus signs_header_cell_0_0_0
Plus and minus signsPlus and minus signs_header_cell_0_1_0
In UnicodePlus and minus signs_header_cell_0_2_0 U+002B + PLUS SIGN (HTML + · +)
U+2212 − MINUS SIGN (HTML − · −)Plus and minus signs_cell_0_2_1
RelatedPlus and minus signs_header_cell_0_3_0
See alsoPlus and minus signs_header_cell_0_4_0 U+00B1 ± PLUS-MINUS SIGN

U+2052 ⁒ COMMERCIAL MINUS SIGNPlus and minus signs_cell_0_4_1

Different fromPlus and minus signs_header_cell_0_5_0
Different fromPlus and minus signs_header_cell_0_6_0 U+002D - HYPHEN-MINUS
U+2010 ‐ HYPHEN 
(many)  - DashPlus and minus signs_cell_0_6_1

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 (which correspond to sum and difference, respectively). Plus and minus signs_sentence_2

Their use has been extended to many other meanings, more or less analogous. Plus and minus signs_sentence_3

Plus and minus are Latin terms meaning "more" and "less", respectively. Plus and minus signs_sentence_4

History Plus and minus signs_section_0

Though the signs now seem as familiar as the alphabet or the Hindu-Arabic numerals, they are not of great antiquity. Plus and minus signs_sentence_5

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: Plus and minus signs_sentence_6

Nicole Oresme's manuscripts from the 14th century show what may be one of the earliest uses of + as a sign for plus. Plus and minus signs_sentence_7

In early 15th century Europe, the letters "P" and "M" were generally used. Plus and minus signs_sentence_8

The symbols (P with overline, p̄, for più (more), i.e., plus, and M with overline, m̄, for meno (less), 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. Plus and minus signs_sentence_9

The + sign is a simplification of the Latin: et (comparable to the evolution of the ampersand &). Plus and minus signs_sentence_10

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. Plus and minus signs_sentence_11

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". Plus and minus signs_sentence_12

They weren't used for addition and subtraction in the treatise, but were used to indicate surplus and deficit; their first use in their modern sense appears in a book by Henricus Grammateus in 1518. Plus and minus signs_sentence_13

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 and minus signs_sentence_14

Plus sign Plus and minus signs_section_1

"+" redirects here. Plus and minus signs_sentence_15

For other uses, see + (disambiguation). Plus and minus signs_sentence_16

The plus sign, +, is a binary operator that indicates addition, as in 2 + 3 = 5. Plus and minus signs_sentence_17

It can also serve as a unary operator that leaves its operand unchanged (+x means the same as x). Plus and minus signs_sentence_18

This notation may be used when it is desired to emphasize the positiveness of a number, especially in contrast with the negative numbers (+5 versus −5). Plus and minus signs_sentence_19

The plus sign can also indicate many other operations, depending on the mathematical system under consideration. Plus and minus signs_sentence_20

Many algebraic structures, such as vector spaces and matrix rings, have some operation which is called, or is equivalent to, addition. Plus and minus signs_sentence_21

It is though conventional to use the plus sign to only denote commutative operations. Plus and minus signs_sentence_22

The symbol is also used in chemistry and physics. Plus and minus signs_sentence_23

For more, see § Other uses. Plus and minus signs_sentence_24

Minus sign Plus and minus signs_section_2

"−" redirects here. Plus and minus signs_sentence_25

It is not to be confused with Hyphen, Hyphen-minus, or Dash. Plus and minus signs_sentence_26

The minus sign, −, has three main uses in mathematics: Plus and minus signs_sentence_27

Plus and minus signs_ordered_list_0

  1. The subtraction operator: a binary operator to indicate the operation of subtraction, as in 5 − 3 = 2. Subtraction is the inverse of addition.Plus and minus signs_item_0_0
  2. The function whose value for any real or complex argument is the additive inverse of that argument. For example, if x = 3, then −x = −3, but if x = −3, then −x = +3. Similarly, −(−x) = x.Plus and minus signs_item_0_1
  3. 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, '−5' names a number the same way 'semicircle' names a geometric figure, with the caveat that 'semi' does not have a separate use as a function name.Plus and minus signs_item_0_2

In many contexts, it does not matter whether the second or the third of these usages is intended. Plus and minus signs_sentence_28

−5 is the same number either way. Plus and minus signs_sentence_29

Sometimes, it does make a difference꞉ the programming language APL uses a raised minus sign ¯, (Unicode U+00AF) as a prefix rather than a function 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 minus sign considered as denoting a function (item 2 above). Plus and minus signs_sentence_30

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. Plus and minus signs_sentence_31

Similarly, in the expression language used by Texas Instruments graphing calculators (at least the early models including the TI-81 and TI-82), a raised minus sign is used in negative numbers (e.g., 3 as the result of 2 − 5). Plus and minus signs_sentence_32

All three uses can be referred to as "minus" in everyday speech, though the binary operator is sometimes read as "take away". Plus and minus signs_sentence_33

In most English-speaking countries, −5 (for example) 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. Plus and minus signs_sentence_34

Further, a few textbooks in the United States encourage −x to be read as "the opposite of x" or "the additive inverse of x"—to avoid giving the impression that −x is necessarily negative (since x itself may already be negative) Plus and minus signs_sentence_35

In mathematics and most programming languages, the rules for the order of operations mean that −5 is equal to −25: Exponentiation binds more strongly than the unary minus, which binds more strongly than multiplication or division. Plus and minus signs_sentence_36

However, in some programming languages (Microsoft Excel in particular), unary operators bind strongest, so in those cases −5^2 is 25, but 0−5^2 is −25. Plus and minus signs_sentence_37

Similar to the plus sign, the minus sign is also used in chemistry and physics. Plus and minus signs_sentence_38

For more, see § Other uses below. Plus and minus signs_sentence_39

Use in elementary education Plus and minus signs_section_3

Some elementary teachers use raised plus and minus signs before numbers to show they are positive or negative numbers. Plus and minus signs_sentence_40

For example, subtracting −5 from 3 might be read as "positive three take away negative 5", and be shown as Plus and minus signs_sentence_41

Plus and minus signs_description_list_1

  • 3 − 5 becomes 3 + 5 = 8,Plus and minus signs_item_1_3

or even as Plus and minus signs_sentence_42

Plus and minus signs_description_list_2

  • 3 − 5 becomes 3 + 5 = 8.Plus and minus signs_item_2_4

Use as a qualifier Plus and minus signs_section_4

In grading systems (such as examination marks), the plus sign indicates a grade one level higher and the minus sign a grade lower. Plus and minus signs_sentence_43

For example, B− ("B minus") is one grade lower than B. Plus and minus signs_sentence_44

In some occasions, this is extended to two plus or minus signs (e.g., A++ being two grades higher than A). Plus and minus signs_sentence_45

Positive and negative are sometimes abbreviated as +ve and −ve. Plus and minus signs_sentence_46

Mathematics Plus and minus signs_section_5

Blood Plus and minus signs_section_6

Blood types are often qualified with a plus or minus to indicate the presence or absence of the Rh factor. Plus and minus signs_sentence_47

For example, A+ means A-type blood with the Rh factor present, while B− means B-type blood with the Rh factor absent. Plus and minus signs_sentence_48

Music Plus and minus signs_section_7

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). Plus and minus signs_sentence_49

For example, "C+" is read "C augmented chord". Plus and minus signs_sentence_50

Sometimes the plus is written as a superscript. Plus and minus signs_sentence_51

Uses in computing Plus and minus signs_section_8

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_sentence_52

Plus and minus signs are often used in tree view on a computer screen—to show if a folder is collapsed or not. Plus and minus signs_sentence_53

In some programming languages, concatenation of strings is written "a" + "b", and results in "ab". Plus and minus signs_sentence_54

In most programming languages, subtraction and negation are indicated with the ASCII hyphen-minus character, -. Plus and minus signs_sentence_55

In APL a raised minus sign (Unicode U+00AF) is used to denote a negative number, as in ¯3. Plus and minus signs_sentence_56

While in J a negative number is denoted by an underscore, as in _5. Plus and minus signs_sentence_57

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. Plus and minus signs_sentence_58

For example, if x equals 6, then y = x++ increments x to 7 but sets y to 6, whereas y = ++x would set both x and y to 7. Plus and minus signs_sentence_59

By extension, ++ is sometimes used in computing terminology to signify an improvement, as in the name of the language C++. Plus and minus signs_sentence_60

In regular expressions, + is often used to indicate "1 or more" in a pattern to be matched. Plus and minus signs_sentence_61

For example, x+ means "one or more of the letter x". Plus and minus signs_sentence_62

Other uses Plus and minus signs_section_9

In physics, the use of plus and minus signs for different electrical charges was introduced by Georg Christoph Lichtenberg. Plus and minus signs_sentence_63

In chemistry, superscripted plus and minus signs are used to indicate an ion with a positive or negative charge of 1 (e.g., NH+ 4 ). Plus and minus signs_sentence_64

If the charge is greater than 1, a number indicating the charge is written before the sign (as in SO2− 4 ). Plus and minus signs_sentence_65

The minus sign is also used, in place of an en dash, for a single covalent bond between two atoms as in the skeletal formula. Plus and minus signs_sentence_66

In the International Phonetic Alphabet, subscripted plus and minus signs are used as diacritics to indicate advanced or retracted articulations of speech sounds. Plus and minus signs_sentence_67

The minus sign is also used as tone letter in the orthographies of Dan, Krumen, Karaboro, Mwan, Wan, Yaouré, , Nyabwa and Godié. Plus and minus signs_sentence_68

The Unicode character used for the tone letter (U+02D7) is different from the mathematical minus sign. Plus and minus signs_sentence_69

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, while a double plus ++ is sometimes used to denote double check. Plus and minus signs_sentence_70

Combinations of the plus and minus signs are used to evaluate a move (+/−, +/=, =/+, −/+). Plus and minus signs_sentence_71

In linguistics, a superscript plus sometimes replaces the asterisk, which denotes unattested linguistic reconstruction. Plus and minus signs_sentence_72

In botanical names, a plus sign denotes graft-chimaera. Plus and minus signs_sentence_73

When writing phone numbers, a plus sign represents the keys required to dial out of a country, such as “00” when calling from the United States. Plus and minus signs_sentence_74

Character codes Plus and minus signs_section_10

Plus and minus signs_table_infobox_1

- + −Plus and minus signs_header_cell_1_0_0
hyphen-minus, plus, minus signs comparedPlus and minus signs_header_cell_1_1_0

Plus and minus signs_table_general_2

ReadPlus and minus signs_header_cell_2_0_0 CharacterPlus and minus signs_header_cell_2_0_1 UnicodePlus and minus signs_header_cell_2_0_2 ASCIIPlus and minus signs_header_cell_2_0_3 in URLPlus and minus signs_header_cell_2_0_4 HTML notationsPlus and minus signs_header_cell_2_0_5
PlusPlus and minus signs_cell_2_1_0 +Plus and minus signs_cell_2_1_1 U+002BPlus and minus signs_cell_2_1_2 +Plus and minus signs_cell_2_1_3 %2BPlus and minus signs_cell_2_1_4 +Plus and minus signs_cell_2_1_5
MinusPlus and minus signs_cell_2_2_0 Plus and minus signs_cell_2_2_1 U+2212Plus and minus signs_cell_2_2_2 Plus and minus signs_cell_2_2_3 %E2%88%92Plus and minus signs_cell_2_2_4 − − −Plus and minus signs_cell_2_2_5
Hyphen-minusPlus and minus signs_cell_2_3_0 -Plus and minus signs_cell_2_3_1 U+002DPlus and minus signs_cell_2_3_2 -Plus and minus signs_cell_2_3_3 %2DPlus and minus signs_cell_2_3_4 Plus and minus signs_cell_2_3_5
Small Hyphen-minusPlus and minus signs_cell_2_4_0 Plus and minus signs_cell_2_4_1 U+FE63Plus and minus signs_cell_2_4_2 Plus and minus signs_cell_2_4_3 %EF%B9%A3Plus and minus signs_cell_2_4_4 ﹣ ﹣Plus and minus signs_cell_2_4_5
Full-width PlusPlus and minus signs_cell_2_5_0 Plus and minus signs_cell_2_5_1 U+FF0BPlus and minus signs_cell_2_5_2 Plus and minus signs_cell_2_5_3 %EF%BC%8BPlus and minus signs_cell_2_5_4 + +Plus and minus signs_cell_2_5_5
Full-width Hyphen-minusPlus and minus signs_cell_2_6_0 Plus and minus signs_cell_2_6_1 U+FF0DPlus and minus signs_cell_2_6_2 Plus and minus signs_cell_2_6_3 %EF%BC%8DPlus and minus signs_cell_2_6_4 - -Plus and minus signs_cell_2_6_5

The hyphen-minus sign, -, is the original ASCII version of the minus sign, which doubles as a hyphen. Plus and minus signs_sentence_75

It is usually shorter in length than the plus sign and often at a different height to the plus-sign's cross bar. Plus and minus signs_sentence_76

It can be used as a substitute for the true minus sign when the character set is limited to ASCII. Plus and minus signs_sentence_77

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. Plus and minus signs_sentence_78

Also several other software programs usable for calculations don't accept the U+2212 minus. Plus and minus signs_sentence_79

For example pasting =3−2 into Excel or 3−2= into the Windows calculator won't work. Plus and minus signs_sentence_80

The true minus is not available on most keyboard layouts. Plus and minus signs_sentence_81

There is a commercial minus sign, ⁒, which is used in Germany and Poland. Plus and minus signs_sentence_82

The symbol ÷ is used to denote subtraction in Norway. Plus and minus signs_sentence_83

For detailed distinctions between minus signs and dashes, see Dash § Similar Unicode characters. Plus and minus signs_sentence_84

Alternative plus sign Plus and minus signs_section_11

See also: Up tack Plus and minus signs_sentence_85

A Jewish tradition that dates from at least the 19th century is to write plus using the symbol ﬩. Plus and minus signs_sentence_86

This practice was adopted into Israeli schools and is still commonplace today in elementary schools (including secular schools) but in fewer secondary schools. Plus and minus signs_sentence_87

It is also used occasionally in books by religious authors, but most books for adults use the international symbol +. Plus and minus signs_sentence_88

The reason for this practice is that it avoids the writing of a symbol + that looks like a Christian cross. Plus and minus signs_sentence_89

Unicode has this symbol at position U+FB29 ﬩ HEBREW LETTER ALTERNATIVE PLUS SIGN. Plus and minus signs_sentence_90

See also Plus and minus signs_section_12

Plus and minus signs_unordered_list_3

  • En dash, a dash that looks similar to the subtraction symbol but is used for different purposesPlus and minus signs_item_3_5
  • Table of mathematical symbolsPlus and minus signs_item_3_6

References and footnotes Plus and minus signs_section_13

Credits to the contents of this page go to the authors of the corresponding Wikipedia page: and minus signs.