Additive identity

The additive identity is the number zero because adding zero to any number leaves that number unchanged.

For example, the sum of three and zero is three.

$$ 3+0 = 3 $$

The same is true when adding five and zero: the sum is five.

$$ 5 + 0 = 5 $$

It is immaterial whether zero appears as the first or the second addend, since addition satisfies the commutative property.

$$ 0+3 = 3+0 = 3 $$

In the case of subtraction, which is the inverse operation of addition, zero functions as a neutral element only when it appears as the subtrahend.

$$ 5 - 0 = 5 $$

And so forth.