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Plus–minus sign
The plus–minus sign or plus-or-minus sign (±) and the complementary minus-or-plus sign (∓) are symbols with broadly similar multiple meanings.
Other meanings occur in other fields, including medicine, engineering, chemistry, electronics, linguistics, and philosophy.
A version of the sign, including also the French word ou ("or"), was used in its mathematical meaning by Albert Girard in 1626, and the sign in its modern form was used as early as 1631, in William Oughtred's Clavis Mathematicae.
In mathematical formulas, the ± symbol may be used to indicate a symbol that may be replaced by either of the plus and minus signs, + or −, allowing the formula to represent two values or two equations.
If x2 = 9, one may give the solution as x = ±3. This indicates that the equation has two solutions: x = +3 and x = −3. A common use of this notation is found in the quadratic formula
which describes the two solutions to the quadratic equation ax2 + bx + c = 0.
Similarly, the trigonometric identity
can be interpreted as a shorthand for two equations: one with + on both sides of the equation, and one with − on both sides.
Plus–minus sign
The plus–minus sign or plus-or-minus sign (±) and the complementary minus-or-plus sign (∓) are symbols with broadly similar multiple meanings.
Other meanings occur in other fields, including medicine, engineering, chemistry, electronics, linguistics, and philosophy.
A version of the sign, including also the French word ou ("or"), was used in its mathematical meaning by Albert Girard in 1626, and the sign in its modern form was used as early as 1631, in William Oughtred's Clavis Mathematicae.
In mathematical formulas, the ± symbol may be used to indicate a symbol that may be replaced by either of the plus and minus signs, + or −, allowing the formula to represent two values or two equations.
If x2 = 9, one may give the solution as x = ±3. This indicates that the equation has two solutions: x = +3 and x = −3. A common use of this notation is found in the quadratic formula
which describes the two solutions to the quadratic equation ax2 + bx + c = 0.
Similarly, the trigonometric identity
can be interpreted as a shorthand for two equations: one with + on both sides of the equation, and one with − on both sides.