Difference between revisions of "Additive inverse"
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If we have: | If we have: | ||
| − | <cmath>a+b=0,</cmath> | + | <cmath>a + b = 0,</cmath> |
| − | we can say that <math>b=-a.</math> | + | we can say that <math>b = -a.</math> |
Thus, <math>b</math> is the additive inverse of <math>a.</math> | Thus, <math>b</math> is the additive inverse of <math>a.</math> | ||
Examples include <math>3</math> and <math>-3</math> or <math>0.5</math> and <math>-0.5.</math> | Examples include <math>3</math> and <math>-3</math> or <math>0.5</math> and <math>-0.5.</math> | ||
| + | |||
| + | == Overview == | ||
| + | In mathematics, the additive inverse of a number <math>a</math> is the number that, when added to <math>a</math>, yields zero. This operation is also known as the opposite (number), sign change, and negation. For a real number, it reverses its sign: the opposite of a positive number is negative, and the opposite of a negative number is positive. Zero is the additive inverse of itself. | ||
| + | |||
| + | The additive inverse of <math>a</math> is denoted by unary minus: <math>-a</math>. For example, the additive inverse of <math>7</math> is <math>-7</math>, because <math>7 + (-7) = 0</math>, and the additive inverse of <math>-0.3</math> is <math>0.3</math>, because <math>-0.3 + 0.3 = 0</math>. | ||
| + | |||
| + | The additive inverse is defined as its inverse element under the binary operation of addition, which allows a broad generalization to mathematical objects other than numbers. As for any inverse operation, the double additive inverse has no effect: <math>-( -x ) = x.</math> | ||
{{stub}} | {{stub}} | ||
| − | [[ | + | |
| + | [[Category:Mathematics]] | ||
Latest revision as of 18:25, 23 July 2025
The additive inverse of a number is the number which sums to 
with the other number.
If we have:
![\[a + b = 0,\]](http://latex.artofproblemsolving.com/4/3/d/43dfb86cb3e9d27bcb76ef0586c39b068ea218b6.png)
we can say that 
Thus, 
is the additive inverse of 
Examples include 
and 
or 
and 
Overview
In mathematics, the additive inverse of a number 
is the number that, when added to , yields zero. This operation is also known as the opposite (number), sign change, and negation. For a real number, it reverses its sign: the opposite of a positive number is negative, and the opposite of a negative number is positive. Zero is the additive inverse of itself.
The additive inverse of is denoted by unary minus: 
. For example, the additive inverse of 
is 
, because 
, and the additive inverse of 
is 
, because 
.
The additive inverse is defined as its inverse element under the binary operation of addition, which allows a broad generalization to mathematical objects other than numbers. As for any inverse operation, the double additive inverse has no effect: 
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