additive identity
The additive identity, in mathematics, refers to the number that, when added to any other number, leaves the original number unchanged
The additive identity, in mathematics, refers to the number that, when added to any other number, leaves the original number unchanged. In other words, it is the number that serves as the neutral element for addition.
The additive identity is denoted by the number 0 (zero). When we add zero to any number, we get the same number as the result. For example:
0 + 7 = 7
0 + (-5) = -5
0 + 0 = 0
In each of these cases, adding zero to the other number does not change the value of the number.
Furthermore, the additive identity has the property that if we add it to any number and then add its additive inverse (opposite), we will get back to zero. This can be expressed as:
a + 0 = a
a + (-a) = 0
For instance:
5 + 0 = 5
5 + (-5) = 0
Both examples show that adding zero or the additive inverse of a number cancels out the effect of the addition operation.
The additive identity is a fundamental concept in mathematics and plays a crucial role in many mathematical properties and operations, such as the commutative and associative properties of addition.
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