Natural Numbers: Definition & Examples

What are Natural Numbers?

Natural numbers are the numbers you use for counting—for example, its definition includes all the positive integers from 1 to infinity. These numbers occur in nature and are the fundamental origins of the number system. Consequently, we see examples of natural numbers all around us in the world.

Notably, the definition of natural numbers does not include zero because counting begins with 1.

Here’s what they look like in set notation and on a number line.

{1, 2, 3, 4, . . ., ∞}

These numbers do not include zero, fractions, decimals, or negative values.

They are counts of occurrences, but they also order items on a number line.

The smallest natural number is 1. The set starts with one as its lowest value, and one is the smallest possible difference between any two values. For example, the closest numbers to 8 are 7 and 9, one less and one more, respectively.

Natural numbers are countably infinite. Countably infinite means that you can count all possible values, but they extend to infinity, as the right arrow on the number line indicates.

Natural Numbers Examples

By definition, you use natural numbers in your daily lives whenever you count something. They quantify and order the basic things in your life.

They allow you to count objects. For example, our house has two cats. They also let you to order items by placing them on the number line. For instance, you can order state populations by the counts of their citizens.

The following are examples of natural numbers:

• The number of cups of coffee you have in the morning.
• The count of steps you walk each day.
• Determining whether Joe or Bob walk more steps.
• The number of people in your class.

Compared to Other Types

Natural numbers are also called counting numbers and ordinal numbers. They are discrete numbers that serve as a contrast to continuous numbers. You count discrete numbers but measure continuous numbers. To learn more, read about discrete vs. continuous data.

The definition of natural numbers are the foundation on which other number types build by extension.

Whole numbers include all counting numbers plus zero, as shown in the Venn diagram. Whole numbers add zero. Zero is a more advanced concept that mathematicians added to number theory relatively recently.

Integers include all counting numbers, their negative values, and zero.

The following sets summarize the various types of discrete numbers:

• Natural Numbers = {1, 2, 3, 4, . . ., ∞}
• Whole Numbers = {0, 1, 2, 3, 4, . . ., ∞}
• Integers = {-∞, . . ., -4, -3, -2, -1, 0, 1, 2, 3, 4, . . ., ∞}