The concept of zero was first defined by a Hindu astronomer and mathematician Brahmagupta in In simple language, zero is a number that lies between the positive and negative numbers on a number line.
Although zero carries no value, it is used as a placeholder. So, zero is neither a positive number nor a negative number. From the above definitions, we can understand that every whole number other than 0 is a natural number. Also, every natural number is a whole number. So, the set of natural numbers is a part of the set of whole numbers or a subset of whole numbers. Let us understand the difference between whole numbers and natural numbers through the table given below:.
The set of natural numbers and the set of whole numbers can be shown on the number line as given below. All the positive integers or the integers on the right-hand side of 0, represent the natural numbers, whereas all the positive integers along with zero, altogether represent the whole numbers. Both sets of numbers can be represented on the number line as follows:.
The basic operations on whole numbers: addition , subtraction , multiplication , and division , lead to four main properties of whole numbers that are listed below:. The sum and product of two whole numbers is always a whole number. The sum or product of any three whole numbers remains the same even if the grouping of numbers is changed.
The sum and the product of two whole numbers remain the same even after interchanging the order of the numbers. This property states that change in the order of addition does not change the value of the sum. It means that the whole numbers are closed under addition. This property also holds true for multiplication, but not for subtraction or division. When a whole number is added to 0, its value remains unchanged, i.
When a whole number is multiplied by 1, its value remains unchanged, i. For example. This property states that the multiplication of a whole number is distributed over the sum of the whole numbers.
It means that when two numbers, take for example a and b are multiplied with the same number c and are then added, then the sum of a and b can be multiplied by c to get the same answer. The same property is true for subtraction as well. All whole numbers are integers and all natural numbers are integers , but not all integers are whole numbers or natural numbers.
For example, -5 is an integer but not a whole number or a natural number. The rational numbers include all the integers, plus all fractions, or terminating decimals and repeating decimals. All natural numbers, whole numbers, and integers are rationals, but not all rational numbers are natural numbers, whole numbers, or integers. We now have the following number classifications: I. Natural Numbers II. Whole Numbers III. Integers IV.
Rationals Numbers can fall into more than one classification. In fact, if a number falls into a category, it automatically falls into all the categories below that category. It includes all the integers and can be expressed in terms of fractions or decimals. Irrational numbers: Irrational numbers are numbers that cannot be expressed in fractions or ratios of integers. It can be written in decimals and have endless non-repeating digits after the decimal point.
What are Whole Numbers? The whole numbers are the numbers without fractions and are a collection of positive integers from 0 to infinity. All the whole numbers exist in number lines. Whole numbers cannot be negative. Examples of whole Numbers Natural numbers are also known as counting numbers including zero are parts of whole numbers, such as 0,1,2,3,4,5, etc. Can negative numbers be whole numbers? Skip to content. Change Language. Related Articles. Table of Contents. Save Article.
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