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
HinduArabic 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:
In Europe in the early 15th century the letters "P" and "M" were
generally used.
The symbols (P with
stroke for piu, i.e. plus) and (M with stroke for meno, i.e.
minus) appeared for the first time in Luca
Pacioli’s mathematics compendium, Summa de Arithmetica,
Geometria, Proportioni et Proportionalita, 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. Widmann referred to the symbols −
and + as
minus and
mer (Modern German
mehr; "more"): "was − ist, das ist minus, und das + ist
das mer".
A book published by
Henricus
Grammateus in 1518 is the earliest found to use + and − for
addition and subtraction.
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 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
emphasise 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 equivalent to,
addition. Moreover, the symbolism has been extended
to very different operations. Plus can mean:
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.
 Directly in front of a number and when it is not a subtraction
operator it means a negative number. For instance −5 is negative
5.
 A unary operator that acts as an instruction to replace the
operand by its opposite. 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.
All three uses can be referred to as "minus" in everyday speech.
When precision is important, −5 is pronounced "negative five"
rather than "minus five"; "minus" is more common for English
speakers born before 1950 and is still popular in some contexts,
but "negative" is usually taught as the only correct reading.
Likewise, textbooks encourage −
x to be read as "the
opposite of
x" or even "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 a raised minus sign is used
in negative numbers (as in 2 − 5 gives
^{−}3),
but such usage is rare.
In mathematics and most programming languages, the rules for the
order of operations mean that
−5
^{2} is equal to −25. Powers bind more strongly than
multiplication or division which binds more strongly than addition
or subtraction. While strictly speaking, the unary minus is not
subtraction, it is given the same place as subtraction. However in
some programming languages and
Excel
in particular, unary operators bind strongest, so in these −5^2 is
25 but 0−5^2 is −25.
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.
In mathematics the
onesided limit
x→
a^{+} means
x approaches
a from the left, and
x→
a^{−}
means
x approaches
a from the right.
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
tree
view on a computer screen to show if a folder is collapsed or
not.
In some programming languages
concatenation of
string is written: "a" + "b" =
"ab", although this usage is questioned by some for violating
commutativity, a property addition is
expected to have.
In most programming languages, subtraction and negation are
indicated with the ASCII
hyphenminus
character,

. In
APL a raised minus sign is used
to denote a negative number, as in
^{−}3) and in
J a negative number is denoted by
an
underscore, 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++.
There is no concept of negative zero in mathematics, but in
computing
−0 may have a separate
representation from zero. In the
IEEE floatingpoint standard
1/−0 is negative infinity whereas 1/0 is positive infinity.
Other uses
The plus and minus signs are also used in phonetic alphabets and
orthographies.
They 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 (U+02D7) is different from the mathematical
minus sign.
Character codes
Plus, minus, and hyphenminus.
Read 
Character 
Unicode 
ASCII 
URL 
HTML (others) 
Plus 
+  U+002B  +  %2B  
''Minus''  −  U+2212    − ''or''
− ''or'' − 
''Hyphenminus''   
U+002D 
 
%2D 

The Unicode minus sign is designed to be the same length and height
as the plus and
equals signs. In most
fonts these are the same width as digits in order to facilitate the
alignment of numbers in tables.
The
hyphenminus sign () is the
ASCII version of the minus sign, and doubles as a
hyphen. 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
ASCII.
There is a
commercial minus sign (⁒), which looks
somewhat like an
obelus, at U+2052 (HTML
&x2052;).
Alternative plus sign
A
Jewish tradition that dates from at least from
the 19th century is to write
plus using a symbol like an
inverted T.
This practice was adopted into Israeli schools
(this practice goes back to at least the 1940s) and is still
commonplace today in elementary
schools (including secular 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 usual
explanation for the origins of this practice is that it avoided the
writing of a symbol "+" that looked like a
Christian cross.
Unicode has this symbol at position U+FB29 "Hebrew
letter alternative plus sign" ( ).
See also
References
 Alan Sangster, Greg Stoner & Patricia McCarthy: "The market
for Luca Pacioli’s Summa Arithmetica" (Accounting, Business &
Financial History Conference, Cardiff, September 2007) p.5
 Earliest Uses of Various Mathematical Symbols
 Hartell, Rhonda L., ed. (1993), The Alphabets of
Africa. Dakar: UNESCO and SIL.
 The Holocaust in Three Generations (Page
107)
 ChristianJewish Dialogue: Theological Foundations
By Peter von der OstenSacken (1986 – Fortress Press – ISBN
0800607716) "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)
 Unicode U+FB29 reference page
External links