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Additive Inverse Calculator
AdditiveInverse Calculator
Definition of “ additiveinverse” : The additiveinverse of a number or an expression is another number or expression such that when they are added together, the sum should be equal to zero.
For example, 1 is the additiveinverse of 1. That is because (1) + (1) = 1 – 1 = 0. Similarly the additiveinverse of x+2 would be –(x+2).
That is because (x+2) + ((x+2)) = x + 2 + (x – 2) = x + 2 – x – 2 = x – x + 2 – 2 = 0 + 0 = 0.
Additiveinverse is also called the opposite.
That means, the additiveinverse of a number n is also called the opposite of the number n.
Formula for Calculating AdditiveInverse:
The formula for finding the additiveinverse of a number or expression is as follows:
Ia = (a), where Ia is the additiveinverse of a and a is any number or expression.
In general terms additiveinverse of any number a is also written as –a.
Proof of Formula of AdditiveInverse:
Suppose there are two numbers a and b that are additiveinverse of each other.
Then by the definition of additiveinverse that we stated above, we can say that,
a + b = 0
Subtracting a from both sides we have:
b = 0 – a
Since the zero (0) on the right side has no value we omit it.
So that now we have:
b = a
But we know that b is the additiveinverse of a (Ia)
So we can say that : Ia = a or Ia =  (a)
Hence proved.
AdditiveInverse Property:
If a set of numbers has elements such that each element has its additiveinverse, then that particular set of numbers is said to obey additiveinverse property.
For example, the set of integers. If we pick an integer, say 5, then its additiveinverse would be 5.
Therefore the additiveinverse of the integer 5 and 5 exist.
Similarly additiveinverses of all integers would exist.
However if we consider the set of natural numbers, we find that the natural number 5 does not have an additiveinverse in the set of natural numbers.
Similarly none of the natural numbers have additiveinverse in the set of natural numbers.
Therefore the set of natural numbers does not obey additiveinverse property.
Except for natural numbers all the other number sets obey additiveinverse property, such as integers, rationals, irrationals, reals, complex, etc.