Closure Property of Integers
According to the integers’ closure property, two integers added together, subtracted from one another, or multiplied together always produce an integer.
- x + y = z
- x – y = z
- x × y = z
So, if x and y ∈ Z, then z ∈ Z.
Note: Since the result of dividing two integers may occasionally not be an integer, the closure property of integers does not apply to the division of integers. For instance, we know that the numbers 3 and 5 are integers, but the result of 3 /5 is 0.60, which is not an integer.
The division of integers falls outside the scope of the closure property. It applies to addition, subtraction, and multiplication of integers.
Let’s examine some of the examples of the integer closure attribute that are provided below:
- -10+ 7 = -3, where {-10, -3, 7} ∈ Z.
- -10- (-8) = -2, where {-10, -8, -2} ∈ Z.
- -7 × 1 = -7, where {-7, 1} ∈ Z.
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