What are Numbers?
We add things or objects using numbers. The numbers 1, 2, 3, … are named as counting numbers or natural numbers. The counting numbers or natural numbers accompanying zero form the set of whole numbers.
An integer is a whole number and not a partial or a decimal number which can be either positive, negative, or zero.
Examples of a few integers are: -5, 1, 5, 8, 97, and 3,657.
The set of integers, is symbolized by the capital letter Z, is represented as follows:
Z = {… -2, -1, 0, 1, 2 …}
The set Z is a denumerable collection. Denumerability is associated with the point that, even though there might be an unlimited number of components in a collection, those elements can be expressed by a list that implies the identification of every component in the set.
What are Integers?
The word integer is developed and termed from the Latin word “Integer” which explains something like an entire. Integers are an original set and consist of whole numbers that include zero, positive numbers, and negative numbers represented on the number line. Integers are expressed by the capital letter Z.
Examples of Integers – 1, 77, 15.
Graphing Integers on a Number Line
- Every number on the right horizontal side is invariably greater than the left side number.
- All positive numbers are placed on the right side of 0, as they are bigger than “0”.
- All negative numbers are placed on the left side of “0”, as they are smaller in value than “0”.
- Zero, which is neither positive nor negative, is placed at the center of the number line.
Integer Mathematical Operations
The four fundamental and elementary arithmetic operations associated with integers are:
- Addition of Integers
- Subtraction of Integer
- Multiplication of Integers
- Division of Integers
Rules of Integers
The foundational and primary rules for integers are stated below:
- The Sum of two particular positive integers is without exception an integer
- The Sum of two given negative integers is without exception an integer
- The product of two given positive integers is without exception an integer
- The product of two given negative integers is without exception an integer
- The Sum of an integer and its respective inverse is without exception equal to zero
- The product of an integer and its reciprocal is without exception equal to 1
Properties of Integers
The most primary and vital characteristics of Integers are stated below:
- Closure Property
- Associative Property
- Commutative Property
- Distributive Property
- Additive Inverse Property
- Multiplicative Inverse Property
- Identity Property
What are Whole Numbers?
The whole numbers are a portion of the number system which includes all the positive numbers from number 0 to infinity. These numbers are an imperative part of the number series. So, they are all actual numbers. We can state that all the whole numbers are real numbers, although not all the real numbers can be termed as whole numbers. The absolute set of natural numbers along with ‘number 0’ are called whole numbers. The examples are: 0, 11, 25, 36, 999, 15998, etc.
These numbers are positive integers consisting of number zero and they do not include incomplete or decimal parts at all. Addition, subtraction, multiplication, division, and all other numerical operations are possible because of the presence of whole numbers.
The symbol used to denote whole numbers is with the character ‘W’ in the capital letter.
W = 0, 1, 2, 3, 4, 5, 6, 45, 8, 9, 2000,…
Fun facts:
- Every natural number is a whole number
- Every counting number is a whole number
- Every positive integer including zero is a whole number
- Every whole number is a real number
Conclusion
Integers and whole numbers are very easy and simple concepts in mathematics, but most of the arithmetic operations are done with the help of their properties and rules.
