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What are natural numbers?

Natural numbers are a fundamental set of numbers in the number system, defined by the following characteristics:

Definition

Natural numbers are the positive integers used for counting and ordering. They start from 1 and continue infinitely2 4 5.

Set Notation

The set of natural numbers is often represented by the symbol (\mathbb{N}) and can be written as: [ \mathbb{N} = {1, 2, 3, 4, 5, \ldots, \infty} ]2 4.

Key Points

Exclusion of Zero: Natural numbers do not include zero (0). The smallest natural number is 11 3 4.
Positive Integers: Natural numbers are only the positive integers, excluding negative numbers, fractions, and decimals1 3 4.
Counting Numbers: They are also known as counting numbers because they are used to count discrete objects1 2 4.
Properties: Natural numbers obey certain properties such as closure under addition and multiplication, but not under subtraction and division4.

Examples

Examples of natural numbers include 1, 2, 3, 4, 5, and so on. For instance, numbers like 23, 56, and 999 are all natural numbers1 3 4.

Difference from Whole Numbers

The main difference between natural numbers and whole numbers is that whole numbers include zero, whereas natural numbers do not. Whole numbers are represented as ({0, 1, 2, 3, \ldots})1 3 4.