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Home > News & Articles > What are Whole numbers: Definition, Concepts, Properties, Even, Odd and Examples
Updated on 29th August, 2023 , 4 min read
All positive integers from 0 to infinity are included in the group of numbers known as whole numbers. The number line contains these figures. Therefore, they are all real numbers. Although not all real numbers are whole numbers, we can say that all whole numbers are real numbers. As a result, the set of natural numbers plus zero can be used to define whole numbers. The category of whole numbers and the negative of natural numbers is known as integers.
All natural numbers and 0 are included in the category of whole numbers. They are a subset of real numbers, which exclude negative numbers, decimals, and fractions. Whole numbers include counting numbers as well. Positive and negative numbers, including zero, are included in integers. Natural numbers, whole numbers, integers, and fractions all fall under the category of real numbers.
To better understand whole numbers, consider the following information:
The letter "W" in uppercase is the symbol used to represent whole numbers. W = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,...
Since the definition of a whole number states that a whole number begins at 0, 0 is the smallest whole number. On a number line, zero sits in the middle of the positive and negative numbers. Although it has no value, zero is used as a stand-in. Therefore, zero is a number that can neither be positive nor negative. There is no "largest" whole number.
We can infer from the definitions given above that all whole numbers other than 0 are natural numbers. All natural numbers are whole numbers, too. As a result, the set of natural numbers is a subset of the set of whole numbers.
Let's use the table below to clarify the distinction between whole numbers and natural numbers:
Whole Number | Natural Number |
The set of whole numbers is, W = {0,1,2,3,...}. | The set of natural numbers is, N = [1, 2, 3,...}. |
The smallest whole number is 0. | The smallest natural number is 1. |
Every natural number is a whole number. | Every whole number is a natural number, except 0. |
The number line can display both the set of whole numbers and the set of natural numbers. The natural numbers are represented by all positive integers, or those on the right-hand side of zero, while all positive integers, including zero, collectively represent the whole numbers.
The whole number can't be negative!
According to the definition, whole numbers are 0, 1, 2, 3, 4, 5, 6, 7,... positive infinity. Negative numbers have no place.
All natural numbers, including zero, are included in the category of whole numbers. So, yes, zero (zero) is the first whole number in addition to being a whole number.
The four fundamental operations on whole numbers—addition, subtraction, multiplication, and division—lead to the following four main characteristics of whole numbers:
A whole number is always the result of two whole numbers when added together. For instance, 7 + 3 = 10 (a whole number), and 7 + 2 = 14.
Even if the order of the numbers is altered, the sum or product of any three whole numbers stays the same. For example, when we add the following numbers, we get the same sum: 10 + (7 + 12) = (10 + 7) + 12 = (10 + 12) + 7 = 29. Similar to that, no matter how the following numbers are grouped, multiplying them produces the same result: 3 × (2 × 4) = (3 × 2) × 4 = 24.
Even after changing the numbers' order, the sum and product of two whole numbers remain the same. According to this property, the value of the sum is unaffected by changes in the order of addition. Let a and b each be a whole number. According to the commutative property, A + B = B + A. For example, if a = 10 and b = 19, then 10 + 19 = 19 + 10 = 29. This property also applies to multiplication, but not to division or subtraction. For example: 7 × 9 = 63, and 9 × 7 = 63.
If a is a whole number, then a + 0 = 0 + a = a, meaning that when a whole number is added to 0, its value does not change. For example, 3 + 0 = 3 + 0 = 3.
A whole number's value does not change when it is multiplied by one, so if a is a whole number, then a 1 = a = 1 a. For example. 4 × 1 = 1 × 4 = 4.
According to this characteristic, a whole number's multiplication is distributed over the sum or difference of the whole numbers. It means that if two numbers, such as a and b, are multiplied by the same number, c, and then added, the result can be obtained by multiplying the sum of a and b by c. This property can be represented as: a × (b + c) = (a × b) + (a × c). Let a = 10, b = 20 and c = 7 ⇒10 × (20 + 7) = 270 and (10 × 20) + (10 × 7) = 200 + 70 = 270. The same characteristic also applies to subtraction. For example, we have a × (b − c) = (a × b) − (a × c). Let a = 10, b = 20 and c = 7 ⇒10 × (20 − 7) = 130 and (10 × 20) − (10 × 7) = 200 − 70 = 130.
A whole number multiplied by 0 always yields a result of 0, i.e., a × 0 = 0 × a = 0. For example, 4 × 0 = 0.
It is not defined how to divide a whole number by zero, so if a is a whole number, a/0 is also not defined.
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By - Nikita Parmar 2023-08-25 09:48:44 , 11 min readAns. The full set of natural numbers, including "0," are referred to as whole numbers. The following are some examples: 0, 11, 25, 36, 999, 1200, etc.
Ans. Whole numbers are the range of numbers that includes zero and natural numbers. not a decimal or fraction. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …}
Ans. The whole numbers are set of real numbers that includes zero and all positive counting numbers, 0 is also a whole number.
Ans. Negative numbers, fractions, and decimals are not considered to be whole numbers.
Ans. The term nonnegative is occasionally used to describe a number that is either positive or zero, whereas nonpositive is sometimes used to describe a number that is either negative or zero because zero is neither positive nor negative. Zero is a neutral number.
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