Natural Numbers

Elementary SchoolMiddle School

Definition

Positive whole numbers that are commonly used for counting and putting things in order. Natural numbers contains no negative numbers or numbers that are in fractions. The numbers 1, 2, 3, 4, 5 demonstrates this. 0 is a number that cannot be universally agreed on whether it is a natural number or not.

Worked examples

\(1, 2, 3, 4, 5, 6, 7, \ldots\)

Natural numbers start at 1 and continue infinitely without fractions or negatives.

\(\)Is \( -3 \) a natural number? No. Is \( \frac{1}{2} \) a natural number? No.\(\)

Natural numbers are only positive whole numbers used for counting.

Common mistakes

\(0\) is always a natural number → \(0\) is not universally agreed upon Some definitions include 0, others don't — check your course's convention.
\(-5\) is a natural number because it's whole → Natural numbers are positive only: \(1, 2, 3, \ldots\) Negative integers are not natural numbers.
\(2.5\) is a natural number → Natural numbers have no fractional parts Only whole counting numbers like 1, 2, 3 are natural.

Where you'll use it next

Natural numbers are the foundation for integers, rational numbers, and real numbers. You'll use them in number theory, set notation, sequences, and any time you classify or count discrete objects in algebra and beyond.

Found in 1 StudyPug lesson

Understanding Number Systems: A Comprehensive Guide

Grade 10 Math

Dive into the world of number systems, from basic counting to complex irrational numbers. Strengthen your mathematical foundation and problem-solving skills with our in-depth explanations and examples.

10th Grade10th