Question

What is the additive identity of integers.
(a) 0
(b) 1
(c) 0.1
(d) 2

Answer 1

Hint: First, start by defining what an additive identity actually is: an additive identity for N is any element e such that for any element n in N, e + n = n = n + e. Using this property, we see that if you add an integer to zero or add zero to an integer, then you get the same integer back. So, 0 is the additive identity of integers.

Complete step-by-step answer:

In this question, we need to find the additive identity of integers.

First, let us start by defining what an additive identity actually is.

In mathematics 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. Let N be a set that is closed under the operation of addition, denoted +. An additive identity for N is any element e such that for any element n in N, e + n = n = n + e.

Using this property, we find the following:

The additive identity property says that if you add an integer to zero or add zero to an integer, then you get the same integer back. The number zero is known as the identity element, or the additive identity. For example, for any integer a,

a + 0 = 0 + a = a

Hence, the additive identity for integers is 0.

So, option (a) is correct.

Note: Note that 0 is the additive identity of not only the integers but also for all the real numbers including rational and irrational numbers. This is a unique but very useful property of the number 0. In this question, it is very important to know and understand about the concept of additive identity.