Additive Inverse Axiom
The additive inverse axiom, also known as the axiom of additive inverses or the axiom of opposites, is a fundamental property in mathematics that deals with the concept of addition
The additive inverse axiom, also known as the axiom of additive inverses or the axiom of opposites, is a fundamental property in mathematics that deals with the concept of addition. Specifically, it states that for every real number a, there exists another real number -a such that their sum is equal to zero.
More formally, the additive inverse axiom can be stated as follows:
For every real number a, there exists a real number -a such that a + (-a) = 0.
In simple terms, this axiom tells us that for any number a, there is a negative number (-a) such that when added to a, their sum is equal to zero. This -a is called the additive inverse of a.
For example, let’s consider the number 5. Its additive inverse would be -5, because 5 + (-5) = 0. Similarly, for the number -3, its additive inverse would be 3, because -3 + 3 = 0.
The additive inverse axiom is a crucial property in mathematics and is used in various areas, such as algebra and calculus. It allows us to perform operations like subtraction by replacing it with addition of the additive inverse.
In summary, the additive inverse axiom states that every real number has an additive inverse, such that their sum is equal to zero.
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