Plus or minus sign

∓

±

The plus or minus sign ( ± ) is a mathematical symbol that is placed in front of a certain expression and means that the value of this expression can be either positive or negative. Often used, for example, to indicate:

limits of change of any parameters;
instrumental accuracy of measurement of a physical quantity;
the expected variation in the values of the statistically measured parameter;
interval of result values in approximate mathematical calculations.

Content

Examples

Example 1: the phrase “mains voltage must be 220 ± 4.5 volts” means that the voltage must be in the range from 215.5 to 224.5 volts.

Example 2, where the symbol “plus or minus” should be understood literally, as an indication of an alternative of two options - the well-known formula for calculating the two roots of a quadratic equation $ax^{2}+bx+c=0$ ${\ displaystyle ax ^ {2} + bx + c = 0}$ :

\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}.

{\ displaystyle \ displaystyle x = {\ frac {-b \ pm {\ sqrt {b ^ {2} -4ac}}} {2a}}.}

This formula is a compact notation combining formulas for the first and second root:

\displaystyle x_{1}={\frac {-b+{\sqrt {b^{2}-4ac}}}{2a}};\quad x_{2}={\frac {-b-{\sqrt {b^{2}-4ac}}}{2a}}

{\ displaystyle \ displaystyle x_ {1} = {\ frac {-b + {\ sqrt {b ^ {2} -4ac}} {2a}}; \ quad x_ {2} = {\ frac {-b- { \ sqrt {b ^ {2} -4ac}}} {2a}}}

Example 3, similar to the second, trigonometric :

\sin(x\pm y)=\sin(x)\cos(y)\pm \cos(x)\sin(y)

{\ displaystyle \ sin (x \ pm y) = \ sin (x) \ cos (y) \ pm \ cos (x) \ sin (y)}

Example 4. Here the interpretation of the plus or minus symbol is different: you must select the sign of the monomial depending on its number in the series:

\sin \left(x\right)=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots \pm {\frac {1}{(2n+1)!}}x^{2n+1}+\cdots

{\ displaystyle \ sin \ left (x \ right) = x - {\ frac {x ^ {3}} {3!} + {\ frac {x ^ {5}} {5!}} - {\ frac {x ^ {7}} {7!}} + \ cdots \ pm {\ frac {1} {(2n + 1)!}} x ^ {2n + 1} + \ cdots}

History

The plus-minus sign appeared in Albert Girard (1626), who wrote down this symbol as follows: ${\boldsymbol {{\underset {-}{\overset {+}{\operatorname {\scriptscriptstyle ou} }}}\ \ }}$ ${\ displaystyle {\ boldsymbol {{\ \ underset {-} {\ overset {+} {\ operatorname {\ scriptscriptstyle ou}}}} \ \}}$ (the French word ou means “ or ”). The modern character of the character gave William Otred in 1631 ^[1] .

Minus Plus Sign

The plus or minus sign has the option: sign $\mp$ ${\ displaystyle \ mp}$ ( minus plus ). It is used in conjunction with one or more plus or minus signs and means that the plus sign in plus or minus strictly corresponds to the minus sign in the minus-plus and vice versa. Example:

\cos(x\pm y)=\cos x\cos y\mp \sin x\sin y

{\ displaystyle \ cos (x \ pm y) = \ cos x \ cos y \ mp \ sin x \ sin y}

This is a compact entry of two formulas:

\cos(x+y)=\cos x\cos y-\sin x\sin y;~\cos(x-y)=\cos x\cos y+\sin x\sin y

{\ displaystyle \ cos (x + y) = \ cos x \ cos y- \ sin x \ sin y; ~ \ cos (xy) = \ cos x \ cos y + \ sin x \ sin y}

Other

In chess notation, the symbol ± means that after the corresponding move, whites have an advantage, and the symbol ∓ - that black has an advantage.

Encoding

Symbol	Code in Unicode	Title in Unicode	Title	HTML hex	HTML ten.	HTML no.
$\pm$ ${\ displaystyle \ pm}$	U + 00B1	Plus-minus sign	Symbol plus or minus	& # x00B1;	& # 177;	& plusmn;
$\mp$ ${\ displaystyle \ mp}$	U + 2213	Minus-or-Plus sign	Minus plus symbol	& # x2213;	& # 8723;

In ISO 8859-1, the plus-minus symbol has the code 0xB1.
In TeX , the plus-minus and minus-plus signs are encoded as \pm and \mp respectively.
In Microsoft Windows, you can enter the plus or minus character by pressing the Alt key and enter the number 0177 on the numeric keypad .
On Linux / Unix systems , you can create a plus or minus symbol with the compose + - sequence.
On Macintosh computers, plus or minus is encoded by entering characters Option ⇧ Shift =.

Notes

↑ Aleksandrova N.V. The History of Mathematical Terms, Concepts, Notation: A Dictionary-Reference. - 3rd ed. - SPb. : LCI, 2008. - p. 127. - 248 p. - ISBN 978-5-382-00839-4 .

[1] Aleksandrova N.V. The History of Mathematical Terms, Concepts, Notation: A Dictionary-Reference. - 3rd ed. - SPb. : LCI, 2008. - p. 127. - 248 p. - ISBN 978-5-382-00839-4 .