| + − | |
|---|---|
Plus and minus signs | |
| In Unicode | U+002B +PLUS SIGN (+) U+2212 −MINUS SIGN (−) |
| Different from | |
| Different from | U+002D -HYPHEN-MINUS U+2010 ‐HYPHEN (many) –Dash |
| Related | |
| See also | U+00B1 ±PLUS-MINUS SIGN U+2213 ∓MINUS-OR-PLUS SIGN |
Theplus sign (+) and theminus sign (−) aremathematical symbols used to denotepositive andnegative functions, respectively. In addition, the symbol+ represents the operation ofaddition, which results in asum, while the symbol− representssubtraction, resulting in adifference.[1] Their use has been extended to many other meanings, more or less analogous.Plus andminus areLatin terms meaning 'more' and 'less', respectively.
The forms+ and− are used in many countries around the world. Other designs includeU+FB29 ﬩HEBREW LETTER ALTERNATIVE PLUS SIGN for plus andU+2052 ⁒COMMERCIAL MINUS SIGN for minus.
Though the signs now seem as familiar as thealphabet or theArabic numerals, they are not of great antiquity. TheEgyptian hieroglyphic sign for addition, for example, resembles 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:[2]
|
Nicole Oresme'smanuscripts from the 14th century show what may be one of the earliest uses of+ as a sign for plus.[3]
In early 15th century Europe, the letters "P" and "M" were generally used.[4][5] The symbols (P with overline,p̄, forpiù (more), i.e., plus, and M with overline,m̄, formeno (less), i.e., minus) appeared for the first time inLuca Pacioli's mathematicscompendium,Summa de arithmetica, geometria, proportioni et proportionalità, first printed and published inVenice in 1494.[6]
The+ sign is a simplification of theLatin:et (comparable to the evolution of theampersand&).[7] The− may be derived from amacron◌̄ written over⟨m⟩ when used to indicate subtraction; or it may come from a shorthand version of the letter⟨m⟩ itself.[8]
In his 1489 treatise,Johannes Widmann referred to the symbols− and+ asminus andmer (Modern Germanmehr; "more"):"[...] was − ist das ist minus [...] und das + das ist mer das zu addirst".[9][10][11] They were not used for addition and subtraction in the treatise, but were used to indicate surplus and deficit; usage in the modern sense is attested in a 1518 book byHenricus Grammateus.[12][13]
Robert Recorde, the designer of theequals sign, introduced plus and minus to Britain in 1557 inThe Whetstone of Witte:[14] "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 abinary operator that indicatesaddition, as in 2 + 3 = 5. It can also serve as aunary operator that leaves itsoperandunchanged (+x means the same asx). This notation may be used when it is desired to emphasize the positiveness of a number, especially in contrast with thenegative numbers (+5 versus −5).
The plus sign can also indicate many other operations, depending on the mathematical system under consideration. Manyalgebraic structures, such asvector spaces andmatrix rings, have some operation which is called, or is equivalent to, addition. It is though conventional to use the plus sign to only denotecommutative operations.[15]
The symbol is also used inchemistry andphysics. For more, see§ Other uses.
The minus sign (−) has three main uses in mathematics:[16]
In many contexts, it does not matter whether the second or the third of these usages is intended: −5 is the same number. When it is important to distinguish them, a raised minus sign (¯) is sometimes used for negative constants, as inelementary education, the programming languageAPL, and some early graphing calculators.[a]
All three uses can be referred to as "minus" in everyday speech, though the binary operator is sometimes read as "take away".[17] In American English nowadays, −5 (for example) is generally referred to as "negative five" though speakers born before 1950 often refer to it as "minus five". (Temperatures tend to follow the older usage; −5° is generally called "minus five degrees".)[18] Further, a few textbooks in the United States encourage −x to be read as "the opposite ofx" or "the additive inverse ofx"—to avoid giving the impression that −x is necessarily negative (sincex itself may already be negative).[19]
In mathematics and most programming languages, the rules for theorder of operations mean that −52 is equal to −25:Exponentiation binds more strongly than the unary minus, which binds more strongly than multiplication or division. However, in some programming languages (Microsoft Excel in particular), unary operators bind strongest, so in those cases−5^2 is 25, but0−5^2 is −25.[20]
Similar to the plus sign, the minus sign is also used inchemistry andphysics. (For more, see§ Other uses below.)
Some elementary teachers use raised minus signs before numbers to disambiguate them from the operation of subtraction.[21] The same convention is also used in some computer languages. For example, subtracting −5 from 3 might be read as "positive three take away negative 5", and be shown as
which can be read as:
or even as
When placed after a number, a plus sign can indicate an open range of numbers. For example, "18+" is commonly used as shorthand for "ages 18 and up" although "eighteen plus", for example, is now common usage.
In USgrading systems, the plus sign indicates a grade one level higher and the minus sign a grade lower. For example,B− ("B minus") is one grade lower thanB. In some occasions, this is extended to two plus or minus signs (e.g.,A++ being two grades higher thanA).[citation needed]
A common trend in branding, particularly with streaming video services, has been the use of the plus sign at the end of brand names, e.g.Google+,Disney+,Paramount+, andApple TV+. Since the word "plus" can mean an advantage, or an additional amount of something, such "+" signs imply that a product offers extra features or benefits.
Positive and negative are sometimes abbreviated as+ve and−ve,[22] and on batteries and cell terminals are often marked with+ and−.
In mathematics theone-sided limitx →a+ meansx approachesa from the right (i.e., right-sided limit), andx →a− meansx approachesa from the left (i.e., left-sided limit). For example, asx → 0+ but asx → 0−.
When placed afterspecial sets of numbers, plus and minus signs are used to indicate that only positive numbers and negative numbers are included, respectively. For example, is the set of all positiveintegers and is the set of all negative integers. In these cases, a subscript 0 may also be added to clarify that 0 is included.
Blood types are often qualified with a plus or minus to indicate the presence or absence of theRh factor. For example, A+ meanstype A blood with the Rh factor present, while B− means type B blood with the Rh factor absent.
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". Sometimes the plus is written as asuperscript.
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 intree view on a computer screen—to show if a folder is collapsed or not.
In some programming languages,concatenation ofstrings is written"a" + "b", and results in"ab".
In most programming languages, subtraction and negation are indicated with the ASCIIhyphen-minus character,-. InAPL a raised minus sign (here written usingU+00AF ¯MACRON) is used to denote a negative number, as in¯3. While inJ a negative number is denoted by anunderscore, as in_5.
InC and some other computer programming languages, two plus signs indicate theincrement 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, theny = x++ increments x to 7 but sets y to 6, whereasy = ++x 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 languageC++.
Inregular expressions,+ is often used to indicate "1 or more" in a pattern to be matched. For example,x+ means "one or more of the letter x". This is theKleene plus notation. Hyphen-minus usually indicates a range ([A-Z] - any capital from 'A' to 'Z'), although it can stand for itself ([ABCDE-] any capital from 'A' to 'E' or '-').
There is no concept of negative zero in mathematics, but in computing−0 may have a separate representation from zero. In theIEEE floating-point standard, 1 / −0 isnegative infinity () whereas 1 / 0 ispositive infinity ().
+ is also used to denote added lines indiff output in thecontext format or theunified format.
In physics, the use of plus and minus signs for differentelectrical charges was introduced byGeorg Christoph Lichtenberg.
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 ). If the charge is greater than 1, a number indicating the charge is written before the sign (as in SO2−
4 ).
A plus sign prefixed to a telephone number is used to indicate the form used forInternational Direct Dialing.[23] Its precise usage varies by technology and national standards. In theInternational Phonetic Alphabet,subscripted plus and minus signs are used as diacritics to indicateadvanced or retracted articulations of speech sounds.
The minus sign is also used as tone letter in the orthographies ofDan,Krumen,Karaboro,Mwan,Wan,Yaouré,Wè,Nyabwa, andGodié.[24] The Unicode character used for the tone letter (U+02D7 ˗MODIFIER LETTER MINUS SIGN) is different from the mathematical minus sign.
The plus sign sometimes represents/ɨ/ in the orthography ofHuichol.[25]
In thealgebraic notation used to record games ofchess, the plus sign+ is used to denote a move that puts the opponent intocheck, while a double plus++ is sometimes used to denotedouble check. Combinations of the plus and minus signs are used to evaluate a move (+/−, +/=, =/+, −/+).
In linguistics, a superscript plus+ sometimes replaces theasterisk, which denotes unattestedlinguistic reconstruction.
Inbotanical names, a plus sign denotesgraft-chimaera.
In Catholicism, the plus sign before a last name denotes aBishop, and a double plus is used to denote an Archbishop.
| - + − | |
|---|---|
hyphen-minus, plus, minus signs compared |
Variants of the symbols have uniquecodepoints in Unicode:
There is acommercial minus sign,⁒, which is (or was) used in Germany and Scandinavia. The symbol÷, still used in many Anglophone countries as adivision sign, is (or was) usedto denote subtraction inScandinavia.[26]
Thehyphen-minus symbol (-) is the form ofhyphen most commonly used in digitaldocuments. On most keyboards, it is the only character that resembles aminus sign or adash so it is also used for these.[27] The namehyphen-minus derives from the originalASCII standard,[28] where it was calledhyphen–(minus).[29] The character is referred to as ahyphen, aminus sign, or adash according to the context where it is being used.
AJewish tradition that dates from at least the 19th century is to writeplus using the symbol﬩, to avoid the writing of a symbol+ that could look like aChristian cross.[30][31] This practice was adopted intoIsraeli schools and is still commonplace today inelementary schools (includingsecular schools) but in fewersecondary schools.[31] It is also used occasionally in books by religious authors, but most books for adults use the international symbol+.Unicode has this symbol at positionU+FB29 ﬩HEBREW LETTER ALTERNATIVE PLUS SIGN.[32]
The minus sign or bar, — , is thought to be derived from the habit of early scribes of using a bar to represent the letter m
{{cite book}}:ISBN / Date incompatibility (help)Loose vs. Precise Semantics. Some ASCII characters have multiple uses, either through ambiguity in the original standards or through accumulated reinterpretations of a limited codeset. For example, 27 hex is defined in ANSI X3.4 as apostrophe (closing single quotation mark; acute accent), and 2D hex as hyphen minus. In general, the Unicode standard provides the same interpretation for the equivalent code values, without adding to or subtracting from their semantics. The Unicode standard supplies unambiguous codes elsewhere for the most useful particular interpretations of these ASCII values; the corresponding unambiguous characters are cross-referenced in the character names list for this block. In a few cases, the Unicode standard indicates the generic interpretation of an ASCII code in the name of the corresponding Unicode character, for example U+0027 is APOSTROPHE-QUOTE'.
The dictionary definition ofplus sign at Wiktionary The dictionary definition ofminus sign at Wiktionary