Identity Property of Integers
According to the identity property of integer addition, the outcome of adding any number to 0 is the same number. For example, if ‘a’ is any number, then a + 0 = 0 + a = a .
Let’s use the negative integer -3 as an example. The result of adding 0 to -3 is -3. The outcome remains unchanged. Therefore, we can state that 0 is the identical element of an integer addition.
Also if 1 is multiplied with an integer, it would result in the same integer. So, 1 is the multiplicative identity element for integers. Any integer can be multiplied by 1 to obtain the same result. As an illustration, a ×1 = 1× a = a.
Note: Integers’ identity property does not apply to division and subtraction operations. If we subtract any integer from 0 in the case of subtraction, we shall obtain that number’s additive inverse. Since ‘a’ can be any integer, a – 0 = a, while 0 – a = -a. If ‘m’ is any integer, then m / 1 = m in the case of division of integers, but 1/ m not equal to m. As a result, there is no identity element for integer division and subtraction.
Properties of Integers
Properties of Integers are the fundamental rules that define how integers behave under various operations such as addition, subtraction, multiplication, and division. As we know, integers include natural numbers, 0, and negative numbers. Integers are a subset of rational numbers, where the denominator is always 1 for integers. Therefore, many of the properties that hold for rational numbers also hold true for integers.
This article explores the concept of Properties of Integers including Closure Property, Associative Property, Commutative Property, Distributive Property, Identity Property, and Inverse Property. So, let’s start learning about all the properties of integers in this article.
Table of Content
- What are the Properties of Integers?
- Closure Property of Integers
- Associative Property of Integers
- Commutative Property of Integers
- Distributive Property of Integers
- Identity Property of Integers
- Inverse Property of Integers