The additive identity of integers is 0.
Understanding Additive Identity
The additive identity is a number that, when added to any integer, leaves the integer unchanged. The term "identity" refers to the fact that the original number's identity stays the same, meaning its value doesn't change after the addition.
Definition
Formally, for any integer a, the additive identity e satisfies the equation:
a + e = a
In the case of integers, e = 0.
Examples
Here are a few examples demonstrating the additive identity with integers:
- 5 + 0 = 5
- -3 + 0 = -3
- 0 + 0 = 0
- 100 + 0 = 100
Why is 0 the Additive Identity?
According to the reference, the additive identity for integers is 0. The reference states that the identity does not change, meaning mathematically, the value remains the same. Therefore, adding 0 to any integer will not change the integer's value, thus satisfying the definition of additive identity.
Additive Identity Explained Simply
Imagine you have a bag of apples. Adding zero apples to the bag doesn't change the number of apples you already have. That's essentially what the additive identity does in mathematics.
