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Updated on 07th August, 2023 , 5 min read
All positive numbers from 1 to infinity are considered to be natural numbers, which make up the entire number system. Because they don't contain zero or negative numbers, natural numbers are also known as counting numbers. They are a subset of real numbers, which only include positive integers and exclude negative, zero, fractional, and decimal numbers.
Natural numbers are all whole numbers with the exception of zero. We frequently use these numbers in our speech and daily activities. Everywhere we look, numbers are used to count things, represent or exchange money, measure temperature, tell the time, etc. These numbers are referred to as "natural numbers" because they are used to count objects. For example, while counting objects, we say 5 cups, 6 books, 1 bottle, and so on.
The numbers that are used for counting and are a subset of real numbers are known as natural numbers. Only positive integers, such as 1, 2, 3, 4, 5, 6,.........., are included in the set of natural numbers.
The positive integers, also referred to as non-negative integers, are a subset of the natural numbers. A few examples are 1, 2, 3, 4, 5, 6,... To put it another way, the set of all whole numbers excluding 0 is known as the "natural numbers."
Natural numbers include 23, 56, 78, 999, 100202, etc.
The answer to this question is ‘No'. Natural numbers are positive integers that range from 1 to infinity, as we already know. However, when we add 0 to a positive integer like 10, 20, etc., it turns into a natural number. In fact, 0 is a whole number which has a null value.
The natural numbers are of two types-
Natural numbers that are odd and fall under the category of set N are known as odd numbers. The collection of odd natural numbers is therefore 1, 3, 5, 7, etc.
The numbers that are even, precisely divisible by 2, and part of the set N are known as even natural numbers. So the set of even natural numbers is {2,4,6,8,...}.
The set of natural numbers is represented in mathematics as 1, 2, 3,... The letter N stands for the collection of natural numbers. N = {1, 2, 3, 4, 5, … ∞}. The smallest natural number is one (1). A set, which in this case refers to numbers, is a grouping of elements. The smallest element in N is 1, and the next element for any element in N is defined in terms of 1 and N. 2 is 1 greater than 1, 3 is 1 greater than 2, and so on. The table below explains the various set forms of natural numbers.
| Statement Form | N = Set of all numbers starting from 1. |
| Roaster Form | N = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ………………………………} |
| Set Builder Form | N = {x : x is an integer starting from 1} |
All whole numbers, with the exception of zero, are considered to be natural numbers. In other words, all whole numbers are not natural numbers, but all natural numbers are whole numbers.
"A part of integers consisting of all natural numbers, except zero," is what is meant by a whole number.
Positive numbers like 1, 2, 3, 4, and so forth make up all natural numbers. They are the numbers you typically count, and they go on forever. All natural numbers, including 0 (i.e., 0, 1, 2, 3, 4, etc.), are considered whole numbers. All whole numbers and their negative equivalent are included in integers. For instance, -4, -3, -2, -1, 0, 1, 2, 3, and so forth. The distinction between a natural number and a whole number is displayed in the following table.
Natural Number | Whole Number |
The set of natural numbers is N= {1,2,3,...∞} | The set of whole numbers is W={0,1,2,3,...} |
The smallest natural number is 1. | The smallest whole number is 0. |
All natural numbers are whole numbers, but all whole numbers are not natural numbers. | Each whole number is a natural number, except zero. |
Every whole number is a natural number. The claim is accurate because whole numbers also include all positive integers, including 0, and natural numbers are the positive integers that range from 1 to infinity.
Four main characteristics of natural numbers are divided into groups, and they are as follows:
The details of each of these attributes are provided below-
Under addition and multiplication, natural numbers are always closed. A natural number will always result from the addition and multiplication of two or more natural numbers. Natural numbers do not adhere to the closure property when it comes to subtraction and division, which means the result of subtracting or dividing two natural numbers might not be a natural number.
Note: If any of the numbers in the case of multiplication and division are not natural numbers, the closure property is not valid. Only the closure property applies to addition and subtraction, though, if the result is a positive number.
For instance:
Not a natural number: -2 x 3 = -6
6/2 = 3, which is not a natural number.
In the case of addition and multiplication of natural numbers, a + (b + c) = (a + b) + c and a (b c) = (a b) c, the associative property holds true. OOn the other hand, the associative property does not apply to the operations of subtracting and dividing natural numbers. n example of this is given below.
The table below provides a summary of the addition, subtraction, multiplication, and division algebraic operations with natural numbers as well as each operation's associated properties.
Properties and Operations on Natural Numbers | |||
Operation | Closure Property | Commutative Property | Associative Property |
Addition | Yes | Yes | Yes |
Subtraction | No | No | No |
Multiplication | Yes | Yes | Yes |
Division | No | No | No |
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By - Nikita Parmar 2023-08-25 09:48:44 , 11 min readAns. Natural numbers are those that begin with 1 when counting. Therefore, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are the first 10 natural numbers.
Ans. 1 is the smallest natural number. We are aware that the smallest element in N is 1 and that we can express the next element in terms of 1 and N (which is 1 greater than the previous element) for each element in N.
Ans. The first three natural numbers on the list are 20, 1555, and 60.
Ans. The first 10 natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 on the number line.
Ans. No, 0 is not a natural number. It is a whole number. Only positive integers are included in natural numbers.
Natural Numbers The numbers that we use when we are counting or ordering {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 …} Whole Numbers The numbers that include natural numbers and zero. Not a fraction or decimal.
0 is not considered a natural number because whole number are start with zero and natural number are start with one. So, zero is a whole number it is not a natural number.
Fractions and decimals are not integers. 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.
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