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The plus and minus signs ( + and ) are mathematical symbols used to represent the notions of positive and negative as well as the operations of and . Their use has been extended to many other meanings, more or less analogous. Plus and minus are terms meaning "more" and "less", respectively.


History
Though the signs now seem as familiar as the 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:
D54 or D55

's manuscripts from the 14th century show what may be one of the earliest uses of the plus sign "+". The birth of symbols – Zdena Lustigova, Faculty of Mathematics and Physics Charles University, Prague

In Europe in the early 15th century the letters "P" and "M" were generally used. The symbols (P with line for più, i.e., plus, and M with line for meno, i.e., minus) appeared for the first time in ’s mathematics compendium, Summa de arithmetica, geometria, proportioni et proportionalità, first printed and published in in 1494. The + is a simplification of the Latin "et" (comparable to the &). The may be derived from a 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 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.

(2018). 9780486204307, Courier Dover Publications.
Earliest Uses of Various Mathematical Symbols

, the designer of the , 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 that indicates , as in 2 + 3 = 5. It can also serve as a that leaves its 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.

(1989). 9780201528213, .
Moreover, the symbolism has been extended to very different operations; plus can also mean:
  • (usually written ⊕): 1 + 1 = 0, 1 + 0 = 1
  • logical disjunction (usually written ∨): 1 + 1 = 1, 1 + 0 = 1


Minus sign
The minus sign ( ) has three main uses in mathematics:
9780884889649, Creative Publications. .
  1. The operator: A to indicate the operation of subtraction, as in 5 − 3 = 2. Subtraction is the inverse of addition.
  2. Directly in front of a number (numeric literal) and when it is not a subtraction operator it means a . For instance −5 is negative 5.
  3. A that acts as an instruction to replace the operand by its . For example, if x is 3, then − x is −3, but if x is −3, then − x is 3. Similarly, −(−2) is equal to 2. The above is a special case of this.

All three uses can be referred to as "minus" in everyday speech. In most English-speaking countries, −5 (for example) is normally pronounced "minus five", but in modern US usage it is instead usually pronounced "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, some 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.

In some contexts, different glyphs are used for these meanings; for instance in the computer language APL and 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), but such usage is uncommon.

In mathematics and most programming languages, the rules for the order of operations mean that −52 is equal to −25: Powers bind more strongly than the unary minus, which binds more strongly than multiplication or division. However, in some programming languages and in particular, unary operators bind strongest, so in those cases −5^2 is 25 but 0−5^2 is −25.


Use in elementary education
Some elementary teachers use raised plus and minus signs before numbers to show they are positive or negative numbers.
(2018). 9781416600350, ACSD Publications.
For example, subtracting −5 from 3 might be read as "positive three take away negative 5" and be shown as

3 − 5 becomes 3 + 5 = 8,
or even as
+3 − 5 becomes +3 + +5 = +8.


Use as a qualifier
In grading systems (such as examination marks), 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 than B. Sometimes this is extended to two plus or minus signs; for example A++ is two grades higher than A.

Positive and negative are sometimes abbreviated as +ve and −ve.

(2018). 9780191039676, Oxford University Press. .
.

In mathematics the xa+ means x approaches a from the right, and xa means x approaches a from the left. For example, when calculating what x−1 is when x approaches 0, because x−1→+∞ when x→0+ but x−1→−∞ when x→0.

are often qualified with a plus or minus to indicate the presence or absence of the ; for instance, A+ means A-type blood with the Rh factor present, while B− means B-type 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". Also used as .


Uses in computing
As well as the normal mathematical usage plus and minus may be used for a number of other purposes in computing.

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

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

In most programming languages, subtraction and negation are indicated with the ASCII character, -. In APL a raised minus sign (Unicode U+00AF) is used to denote a negative number, as in ¯3. While in J a negative number is denoted by an , as in _5.

In C and some other computer programming languages, two plus signs indicate the increment operator and two minus signs a decrement. For example, x++ means "increment the value of x by one" and x-- means "decrement the value of x by one". By extension, "++" is sometimes used in computing terminology to signify an improvement, as in the name of the language C++.

In regular expressions, "+" is used to indicate "1 or more" in a pattern to be matched. For example, "x+" 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 (∞).


Other uses
In chemistry, the minus sign (rather than an ) is used for a between two atoms, as in the .

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 , , Karaboro, , , Yaouré, Wè, and .Hartell, Rhonda L., ed. (1993), The Alphabets of Africa. Dakar: UNESCO and SIL. The Unicode character used for the tone letter (U+02D7) is different from the mathematical minus sign.

In the algebraic notation used to record games of , the plus sign (+) is used to denote a move that puts the opponent into check. A double plus (++) is sometimes used to denote . Combinations of the plus and minus signs are used to evaluate a move (+/−, +/=, =/+, −/+).


Character codes
+
%2B
+
%E2%88%92
− − −

The hyphen-minus sign (-) is the alternative/version of the minus sign, and doubles as a . It is usually shorter in length than the plus sign and sometimes at a different height. It can be used as a substitute for the true minus sign when the character set is limited to . 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.

There is a commercial minus sign (⁒), which looks somewhat like an , at U+2052 (HTML ⁒).

The - entity is HTML 5.


Alternative plus sign
A tradition that dates from at least the 19th century is to write plus using a symbol like an inverted T. This practice was adopted into schools and is still commonplace today in elementary schools (including schools) but in fewer . Christian-Jewish Dialogue: Theological Foundations By Peter von der Osten-Sacken (1986 – Fortress Press) "In Israel the plus sign used in mathematics is represented by a horizontal stroke with a vertical hook instead of the sign otherwise used all over the world, because the latter is reminiscent of a cross." (Page 96) 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 . has this symbol at position . Unicode U+FB29 reference page This form of the plus sign is also used on the control buttons at individual seats on board the El Al Israel Airlines aircraft.


See also
  • for the meaning of + in
  • List of international call prefixes that + can represent the numbers required to dial out of a country as seen in a phone number
  • Table of mathematical symbols
  • , a dash that looks similar to the subtraction symbol but is used for different purposes
  • , the star mark denoting unattested linguistic reconstructions, is sometimes replaced by a superscript plus


References and footnotes
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