Plus-minus sign
|
|
The plus-minus sign (±) is a mathematical symbol commonly used to indicate the precision of an approximation, or as a convenient shorthand for a quantity with two possible values.
This second usage is perhaps most commonly encountered in the well-known formula for the solutions of quadratic equations: if <math>ax^2 + bx + c = 0<math>, then
- <math>
x = \frac{-b \pm \sqrt {b^2-4ac\ }}{2a}. <math> In other words, the two solutions to the equation are
- <math>
x = \frac{-b + \sqrt {b^2-4ac\ }}{2a} <math> and
- <math>
x = \frac{-b - \sqrt {b^2-4ac\ }}{2a} <math>
but using the ± symbol allows us to compress these expressions into a single formula.
The use of ± for an approximation is closely related. For example, "5 ± 0.2" denotes a quantity that is within 0.2 units of 5; it is between 5 − 0.2 and 5 + 0.2.
There is also another character, minus-or-plus sign (∓); This is rarely seen; it can be used alongside "±" in such expressions as "x ± y ∓ z", which can be interpreted as "x + y − z" or "x − y + z", but not "x + y + z" nor "x − y − z". The upper "−" in "∓" is considered attached to the "+" of "±" (and the lower symbols work in the same way) even though there is no visual indication of the dependency. In this simple case the original expression can be rewritten as "x ± (y − z)" to avoid confusion, but more complex cases such as the trig identity "cos(x±y) ≡ cos(x)cos(y) ∓ sin(x)sin(y)" cannot be rewritten this way.
In ISO-8859-1,7,8,9,13,15 and 16, the plus-minus symbol is given by the code B1hex Since the first 256 code points of Unicode are identical to the contents of ISO-8859-1 this symbol can be found at Unicode code point Template:Uplusfirst00B1. The symbol also has a HTML entity representation of ±. The rarer minus-or-plus sign (∓) is not generally found in legacy encodings but is available in Unicode with codepoint U+2213.
In a pinch, a crude version of these symbols can also be formed by underlining/overlining a + sign ( + + ).fr:Signe plus ou moins