Natural Numbers

Table of Contents

Natural Numbers – Definition: A natural number is any positive integer. It is denoted by the symbol N. The first few natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.

Whole Numbers and Natural Numbers

A whole number is any number that can be expressed as a whole number, while a natural number is any number that is greater than zero. Whole numbers are always positive, while natural numbers can be positive or negative. The set of whole numbers includes the natural numbers, while the set of natural numbers does not include the whole numbers.

Set of Natural Numbers

A set of natural numbers is a set of positive whole numbers, including 0. The set of natural numbers is denoted by N.
The numbers in the set of natural numbers are:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100.

Properties of the Natural Number

Positive integers have many properties that make them unique mathematical objects. Some of these include:

Natural numbers are whole numbers that are positive.
They are used to count discrete objects.
The first natural number is 1 and the next is 2.
Every natural number has a unique successor.
Natural numbers can be divided by 1 and themselves only.
The sum of two natural numbers is always a natural number.
The product of two natural numbers is always a natural number.
Natural numbers are closed under addition and multiplication.
Every natural number has a unique factorization into primes.

1. Closure Property

The Closed property of the OutlookItem class indicates whether the item is closed.
The Closed property is a read-only Boolean value that indicates whether the OutlookItem is closed.

2. Associative Property

The associative property states that when two or more numbers are multiplied together, the order of the numbers does not matter as long as the parentheses are correct. For example, 5 × (6 + 8) = (5 × 6) + (5 × 8).

3. Commutative Property

The commutative property states that the order of numbers (or any other objects) does not affect the result of an operation. This property is symbolized by the equation a + b = b + a.

For example, 3 + 5 = 5 + 3 and 2x + 3 = 3x + 2.

4. Distributive Property

For any three real numbers a, b, c:

a + (b + c) = (a + b) + c

a × (b × c) = (a × b) × c

The natural numbers, also known as the positive integers, are the set of numbers {1, 2, 3, 4, 5, …}. Here are some properties of the natural numbers:

The natural numbers are closed under addition and multiplication. This means that if you add or multiply two natural numbers, the result will always be a natural number.
The natural numbers are not closed under subtraction or division. This means that if you subtract or divide two natural numbers, the result may not be a natural number.
Every natural number has a unique successor. This means that if you add 1 to a natural number, you will always get a different natural number.
The natural numbers are well-ordered. This means that there is a first natural number (1) and every natural number has a successor.
The natural numbers are infinite. This means that there is no largest natural number.

Smallest Natural Number

The smallest natural number is 1.