The plusminus sign (±) is a mathematical symbol commonly used to indicate the precision of an approximation, or as a convenient notation for a value that can be of either sign.
In mathematics, the sign is pronounced "plus or minus" and indicates that there are two possible answers: one positive, and one negative. In most experimental sciences, the sign is pronounced "give or take" and indicates an inclusive range of values that a reading might have.^{[citation needed]}
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The use of ± for an approximation is most commonly encountered for presenting the numerical value of a quantity together with its tolerance or its statistical margin of error. For example, "5.7±0.2" denotes a quantity that is specified or estimated to be within 0.2 units of 5.7; it may be anywhere in the range from 5.7 − 0.2 (i.e. 5.5) to 5.7 + 0.2 (5.9). More precisely, in scientific usage it usually comes with a probability of being within the interval, usually that of 1 or 2 standard deviations (68.3% or 95.4%).
A percentage may also be used to indicate the error margin. For example, 230 ± 10% V refers to a voltage within 10% of either side of 230 V (207 V to 253 V). Separate values for the upper and lower bounds may also be used. For example, to indicate that a value is most likely 5.7 but may be as high as 5.9 or as low as 5.6, one could write 5.7+0.2−0.1.
In mathematical equations, the use of ± may be found as shorthand, to present two equations in one formula: equation+ OR equation represented with equation±.
A wellknown example is offered by the quadratic formula:
If ax^{2} + bx + c = 0 then
Written out in full, this states that there are two solutions to the equation, i.e. that
Another example is found in the trigonometric identity
This stands for two identities: one with "+" on both sides of the equation, and one with "−" on both sides.
A somewhat different use is found in this presentation of the formula for the Taylor series of the sine function:
This mild abuse of notation is meant to indicate that the sign of the terms alternate, where (starting the count at 0) the terms with an even index n are added while those with an odd index are subtracted. A less ambiguous presentation in this case would use the quantity (−1)^{n}, which gives +1 when n is even and −1 when n is odd.
There is another character, the minusplus sign (∓), which is seen less often. It only takes on significant meaning when used in conjunction with the "±" sign. It can be used alongside "±" in such expressions as "x ± y ∓ z", which can be interpreted as "x + y − z" or/and "x − y + z", but neither "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. The original expression can be rewritten as "x ± (y − z)" to avoid confusion, but cases such as the trigonometric identity
are most neatly written using the "∓" sign.
±
.∓
\pm
and \mp
entities, respectively.
