# Plus minus sign

± ∓
Mathematical signs
arithmetic
Plus sign +
Minus sign - , ./.
Mark , ×
Divided sign : , ÷ , /
Plus minus sign ± ,
Comparison sign < , , = , , >
Root sign
Percent sign %
Analysis
Sum symbol Σ
Product mark Π
Difference sign , Nabla ,
Prime
Partial differential
Integral sign
Concatenation characters
Infinity symbol
geometry
Angle sign , , ,
Vertical , parallel ,
Triangle , square ,
Diameter sign
Set theory
Union , cut ,
Difference , complement ,
Element character
Subset , superset , , ,
Empty set
logic
Follow arrow , ,
Universal quantifier
Existential quantifier
Conjunction , disjunction ,
Negation sign ¬

The plus minus sign (±) and the minus plus sign (∓) are symbols from mathematics . On the one hand, they can be used to express that a term in a mathematical expression can be both positive and negative (for example, “± 5” means that the number under consideration can be +5 or −5). On the other hand, the plus-minus sign in front of a number can be used to designate the entire range of numbers enclosed by the positive and negative value of the number (so “± 5” denotes the range from −5 to +5 including these values ​​themselves).

## typography

The plus minus sign mostly consists of the unchanged form of the plus sign from the same font with a minus sign underneath , which has the same shape as the horizontal bar of the plus sign. In most cases, a distance is left between the components that is less than the line width; there are also shapes in which the components touch. With the minus plus sign, the minus sign is placed in the same way above the plus sign. The vertical position of the characters in the typographic line system is inconsistent.

## use

### Technology and commerce

In technology, the plus-minus sign denotes uncertainties or tolerances . For example, “5 cm ± 0.05 cm” means that the actual length can be between 4.95 cm and 5.05 cm. The notation with regard to character spacing is inconsistent; may also be carried out without a gap afterwards, an identical unit of measurement does not have to be repeated, the dimension and the deviation are often written with the same number of decimal places (accuracy): "15.00 ± 0.05 cm" or "15.00 ± 0, 05 cm ". The unit of measurement can be omitted on plans with the standard unit of measure listed: "Dimensions in mm. ... 304.80 ± 6.35 ".

Similarly, can be expressed in the merchant being that a thing with a deficiency is associated, when the value of a measurable size (e.g., weight. Length) is outside the specified range so.

### mathematics

#### Formula collections

Often the two characters are used in formulas to combine two similar formulas to save space. This is illustrated here using the example of the formulas from the addition theorems of trigonometry . In compact notation, the two formulas are

${\ displaystyle \ sin (x \ pm y) = \ sin x \; \ cos y \ pm \ sin y \; \ cos x.}$ Either the upper sign (+) or the lower sign (-) must be selected on both sides. This means that when adding and on the left side must also be added on the right side. If you subtract and , the right side is also subtracted. The compact notation thus contains the two equations ${\ displaystyle x}$ ${\ displaystyle y}$ ${\ displaystyle x}$ ${\ displaystyle y}$ ${\ displaystyle \ sin (x + y) = \ sin x \; \ cos y + \ sin y \; \ cos x}$ and
${\ displaystyle \ sin (xy) = \ sin x \; \ cos y- \ sin y \; \ cos x.}$ The expression
${\ displaystyle \ cos (x \ pm y) = \ cos y \; \ cos x \ mp \ sin x \; \ sin y}$ means, on the other hand, that when adding from and on the right side must be subtracted and that when subtracting from and on the right side must be added . So it is a summary of the two equations ${\ displaystyle x}$ ${\ displaystyle y}$ ${\ displaystyle x}$ ${\ displaystyle y}$ ${\ displaystyle \ cos (x + y) = \ cos y \; \ cos x- \ sin x \; \ sin y}$ and
${\ displaystyle \ cos (xy) = \ cos y \; \ cos x + \ sin x \; \ sin y}$ .

#### Square root

The plus minus sign is often used for square root extraction (pulling the root). For example, because both is and is, you write . The equation therefore has the two real numbers and as a solution. As a shorthand you write for it . ${\ displaystyle (-2) ^ {2} = 4}$ ${\ displaystyle 2 ^ {2} = 4}$ ${\ displaystyle (\ pm 2) ^ {2} = 4}$ ${\ displaystyle x ^ {2} = 4}$ ${\ displaystyle x_ {1} = 2}$ ${\ displaystyle x_ {2} = - 2}$ ${\ displaystyle x_ {1/2} = \ pm {\ sqrt {4}} = \ pm 2}$ ### chemistry

In chemistry - especially in stereochemistry - the plus minus sign is used as a prefix to denote racemates , which are 1: 1 mixtures of two enantiomers , one of which rotates the plane of polarized light in the polarimeter to the right and the other to the left.

### physics

In physics and related sciences (e.g. astronomy) the plus-minus sign is used to indicate uncertainties, for example in measurement results and other dimensions. The standard deviation is usually given . Depending on the context, it is then stated that 68% of all measured values ​​lie in the specified interval, or that the specified value for the specified variable lies with a probability of 68% in the specified interval (the confidence range ).

### chess

When commenting on a game of chess , both signs indicate a position evaluation:

± : White is much better
: Black is much better

## Representation in computer systems

International character  coding standard Unicode
and coding in the Internet document format HTML
character Unicode designation HTML Latex
position designation hexadecimal decimal named
± U + 00B1 plus-minus sign Plus minus sign & # x00B1; & # 0177; & plusmn; \pm
U + 2213 minus-or-plus sign Minus plus sign & # x2213; & # 8723; \mp

In ASCII - character set from the year 1963 the plus minus sign is not, which is why many older computer systems could not represent it. However, it was already included in the 1986 ASCII extension ISO 8859-1 (also known as Latin-1) . Almost all modern computers use the Unicode standard introduced in 1991 and can therefore process and display both characters without any problems.

If you want to enter the plus minus sign under Microsoft Windows , hold down the Alt key and type “0177” on the number pad. On Unix systems (such as Linux) the plus minus sign can often be generated by pressing the Compose key followed by +, followed by -.

## Individual evidence

1. Scott Pakin: The Comprehensive LaTeX Symbol List. WM (PDF, 8.7 MB), September 28, 2017, accessed on September 28, 2017 (English).