Question & Answer

What is an additive identity of a set ?

ANSWER Verified Verified
Hint: To solve this question we will first of all define what is an additive identity. The additive identity of a set that is equipped with the operation of addition is an element which, when added to any element x in the set, yields x.

Complete step-by-step solution -
As defined above an additive identity property says that if you add a real number to zero or add zero to a real number, then you get the same real number back. The number zero is known as the identity element, or the additive identity.
Therefore, we get that the "Additive Identity" is 0, because adding 0 to a number does not change it.
Let a be any real number then we make the following argument for a number to satisfy the criteria to become additive identity.
a + 0 = 0 + a = a
For example,
5 + 0 = 0 + 5 = 5.
Hence, we got the additive identity of real numbers is 0.

Note: The possibility of error in such a type of question can be at a point where a different set is defined. For the set of real numbers, the additive identity is 0 but for the set of natural numbers there does not exist any additive identity because 0 does not belong to the set of natural numbers.