What Do You Mean By Numbers?
A number system is a writing system that frequently uses numbers or other symbols to describe a certain set. It provides a unique representation of each number and the arithmetic and algebraic structure of the figures. It also allows us to perform arithmetic operations like addition, subtraction, and division. Let us now know in this article about the meaning and properties of whole numbers, which are a part of the number system.
Whole Numbers Definition
The whole numbers are numbers without fractions. They are a set of positive integers and zero. Whole numbers are shown as ‘W’ and the number set is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,…………}.
Including zero, all figures are true and do not include either fractional or decimal sections i.e. 3/4, 2.2, or 5.5 are not entire quantities. So, these are not whole numbers. Furthermore, with all the numbers, subtraction, multiplication, and division operations are necessary.
If you are in trouble again, what is the actual amount in mathematics? The accompanying explanation offers a more comprehensive understanding of the whole count.
An integer that is 0 and greater than 0 is a whole sum. The first five numbers in all were 0, 1, 2, 3, and 4. They all go up to infinity.
The whole numbers are almost the same as natural numbers except for 0. Since integers range from negative infinity to positive infinity, total whole numbers are a subset of integer numbers.
The whole number set is expressed by using the basic mathematical definition of a set W = {0, 1, 2, 3,…..} as a collection of objects that share a well-defined property. Beginning with 0, the element x of the set is created by adding the number before x to its predecessor, which is x-1. Using an ellipsis (...) implies the number of elements in the set is not finite (i.e., infinite).
With the exception of 0, every number x has precisely one immediate predecessor — the amount that falls before x. Each number y has exactly one immediate counterpart — the number after y.
An interesting feature of the whole set of numbers is that there is no largest whole number. Suppose b is the highest whole number, so b + 1 is a whole number. Nevertheless, b + 1 is greater than b. This approach reveals that you can always find a bigger whole number.
Whole Numbers Properties
Complete number properties are based on mathematical operations such as combining, subtracting, splitting, and multiplying. If inserted, subtracted or combined; two whole numbers may form the entire number itself. As a result, we can also get a fraction in the division method. Here are different properties of whole numbers.
Closure Property
Combining the two whole numbers forms a whole number. i.e. if x and y are two entire numbers then x × y or x + y is an entire number, too.
Commutative Property of Addition and Multiplication
The sum and product of any of the two whole numbers are the same regardless of the order in which they are added or multiplied, i.e. if x and y are two full numbers x + y = y + x and x × y = y × x.
Additive Identity
If a whole number is added to 0, its value remains unchanged, i.e. when x is a whole number then the equation can be written as:
x + 0 = 0 + x.
Associative Property
When adding or multiplying whole numbers as a set, they can be grouped in any order, and the result will be the same, i.e. if x, y, and z are full numbers then the equation can be expressed as
x + (y + z) = (x + y) + z
And,
x · (y · z) = (x · y) · z
Distributive Property
When x, y, and z are three complete digits, the multiplication over distributive property is given by:
x × (y + z) = (x × y) + (x × z)
Likewise, the multiplication over subtraction distribution property is given by:
x × (y - z) = (x × y) - (x × z)
Can Whole Numbers
The whole number cannot be negative! The reason for the same has been stated below:
As per the definition of whole numbers, the number line as stated {0, 1, 2, 3, 4, 5, 6... till positive infinity} are constituted in the whole numbers line.
There is no place for negative numbers in the whole numbers line.
Is 0 a Whole Number?
The set of numbers contains all the natural numbers, along with zero. So yes, 0 (zero) is not only a whole number but it is also the first whole number.
Multiplication by Zero
By multiplying a whole number with 0, the answer will always be 0, i.e. X × 0 = 0 × X = 0.
Division by Zero
The whole number division by 0 is not specified, i.e. when x is a whole number, x/0 is not defined.
Some Facts About the Whole Numbers
There is no single number that can be called ‘big’.
Besides 0, all values have an immediate predecessor or a number that falls before them.
There is a decimal number or a percentage for two whole quantities, but not whole numbers.
Difference Between Whole Numbers and Natural Numbers
FAQs on Whole Numbers
1. How can you represent whole numbers on a number line and how can you use this number line to perform addition in a number?
In order to represent whole numbers on a number line, you first need to draw a line and label it as 0. Now, mark the points on the right of 0 as 1, 2, 3, 4, and so on. Make sure that you mark these points at an equal distance from each other. This way you can represent whole numbers to whatever you want to. This number line can be used to perform simple mathematical calculations like addition, subtraction, and multiplication.
In order to add two whole numbers using a number line, firstly, draw a number line. Now, if you need to add ‘n’ to a number, then you need to make ‘n’ jumps to the right. For example, if you need to add 4 to 3, then you should make 4 jumps to the right of 3 to get the desired result, which is 7.
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2. How can you use the number line to perform subtraction on a given whole number?
In order to perform subtraction of whole numbers on a number line, you first need to draw a number line and represent the whole numbers clearly. Now, if you need to subtract ‘n’ from a given number, then simply jump n times to the left of that number, for example, if you need to subtract 2 from 4, then jump 2 times to the left of 4, which will be 2.
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3. How can I perform the multiplication of two whole numbers using a number line?
In order to perform multiplication of two whole numbers, you need to first draw a number line and then start from 0, now jump n spaces to the right m times in order to calculate n X m. For example, if you need to multiply 3 with 5, then you should jump 5 steps starting from 0 and repeat it 3 times to find the final result which is 15.
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4. What are the key points related to whole numbers?
Whole numbers are the numbers that we use for counting, that is 0, 1, 2, 3, and so on. If you add a number to a whole number, you will get the successor of that number and if you subtract a number from a given number, then you will get the predecessor of that number. There is no whole number or natural number which does not have a successor. 0 is the only whole number that does not have a predecessor. The set of natural numbers and whole numbers is the same, except that the set of natural numbers does not contain 0 but whole numbers do.
The number line is one of the best ways to represent whole numbers that can also be used for performing mathematical calculations. Moving towards the right of a number in the number line allows addition whereas moving towards the left gives the result of subtraction. For multiplying two numbers on a number line we need to make jumps starting from 0.
Whole numbers are also represented in the form of patterns which is not only interesting to learn but also helps in performing calculations verbally and also in understanding the properties of whole numbers in a much better way.
5. Can whole numbers be negative?
The entire numbers are a collection of real numbers that include zero as well as all positive counting numbers. However, it does not include fractions, negative integers, fractions, or decimals. Because integers comprise both positive and negative numbers, all whole numbers are also integers. However, the converse is not true, i.e., all integers do not have to be whole numbers because they also include negative values, which are not included in whole numbers. As a result, negative numbers are not regarded as whole numbers since whole numbers are a collection of real numbers that do not include negative numbers, fractions, or decimals.
6. What are the different properties of whole numbers?
The whole numbers have four major properties, that is, closure property, associative property, commutative property, and distributive property. The closure property of whole numbers states that when the two whole numbers are added or multiplied, then the result of such a calculation is always a whole number. According to the associative property of whole numbers, when addition and multiplication calculation is applied on three or more whole numbers, then whichever way you group these whole numbers the result will remain the same. According to the commutative property of whole numbers, while calculating the sum or product of three or more whole numbers, the resultant of the calculation will remain the same even if you change the order of these whole numbers. The distributive property of the whole numbers states that a calculation can be calculated in two ways if the equation involves addition as well as multiplication. You can either multiply a and b with c and then add the product of the two, or you can add a and b and divide the sum with c, though the resultant in both the cases will remain the same.