Difference between revisions of "Additive Inverse"
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| − | In mathematics, the additive inverse of a number a is the number that, when added to a | + | #REDIRECT [[Additive inverse]] |
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| + | == Overview == | ||
| + | In mathematics, the additive inverse of a number a is the number that, when added to a yields zero. This operation is also known as the opposite (number), sign change, and negation.[1] For a real number, it reverses its sign: the opposite of a positive number is negative, and the opposite to a negative number is positive. Zero is the additive inverse of itself. | ||
The additive inverse of a is denoted by unary minus: −a (see the discussion below). For example, the additive inverse of 7 is −7, because 7 + (−7) = 0, and the additive inverse of −0.3 is 0.3, because −0.3 + 0.3 = 0 . | The additive inverse of a is denoted by unary minus: −a (see the discussion below). For example, the additive inverse of 7 is −7, because 7 + (−7) = 0, and the additive inverse of −0.3 is 0.3, because −0.3 + 0.3 = 0 . | ||
| − | The additive inverse is defined as its inverse element under the binary operation of addition (see the discussion below), which allows a broad generalization to mathematical objects other than numbers. As for any inverse operation, double additive inverse has no effect: −(−x) = x. | + | The additive inverse is defined as its inverse element under the binary operation of addition (see the discussion below), which allows a broad generalization to mathematical objects other than numbers. As for any inverse operation, the double additive inverse has no effect: −(−x) = x. |
Latest revision as of 19:25, 23 July 2025
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Overview
In mathematics, the additive inverse of a number a is the number that, when added to a yields zero. This operation is also known as the opposite (number), sign change, and negation.[1] For a real number, it reverses its sign: the opposite of a positive number is negative, and the opposite to a negative number is positive. Zero is the additive inverse of itself.
The additive inverse of a is denoted by unary minus: −a (see the discussion below). For example, the additive inverse of 7 is −7, because 7 + (−7) = 0, and the additive inverse of −0.3 is 0.3, because −0.3 + 0.3 = 0 .
The additive inverse is defined as its inverse element under the binary operation of addition (see the discussion below), which allows a broad generalization to mathematical objects other than numbers. As for any inverse operation, the double additive inverse has no effect: −(−x) = x.
