Natural numbers

Natural numbers, also referred to as counting numbers, are the numbers 1, 2, 3, 4, 5, up through infinity. They are the numbers we use for counting objects and do not include negative numbers, fractions, decimals, etc. They are non-negative integers. Depending on the definition being used, the number 0 may or may not be included as part of the natural numbers. In some cases, the set of natural numbers, including 0, is referred to as whole numbers.

There is a lot of overlap between definitions of various sets of numbers. As mentioned, natural numbers are part of whole numbers. They are also included within integers, real numbers, cardinal numbers, ordinal numbers, nominal numbers, and more.

Natural numbers can be represented on a number line as follows:

The above number line uses the definition of natural numbers that doesn't include 0. The arrow at the end of the ray indicates that the line extends infinitely, with each tick mark representing one of the natural numbers.

Natural numbers, counting, and basic operations

Natural numbers are often used as part of an introduction to numbers, counting, and basic operations such as addition and subtraction. This is because they are relatively simple to work with, since they don't involve concepts like negative numbers, allowing a person new to numbers to focus on learning new concepts before delving into other classifications of numbers.


One common way counting is taught is through finger counting where each finger represents one digit. Depending on region, the thumb or index finger may be used to represent the number 1.

In cases where the thumb represents 1, the index finger is 2, the middle finger is 3, the ring finger is 4, and the pinky is 5. The second hand is then used, with the thumb starting as 6, and the pinky being 10.

In cases where the index finger represents 1, the middle finger is 2, the ring finger is 3, the pinky is 4, and the thumb is 5. The second hand is then used, with the index finger starting as 6, and the thumb being 10.

Other systems may be used as well, but these are two of the most common. In either case, a person who is counting to 10 would start on one hand with a closed fist, raising each finger based on the preferred system as they count up to 10.

Basic operations

Natural numbers along with finger counting can also be used as a starting point for learning addition and subtraction. There are a number of different ways this could be done, but generally, people can raise or lower fingers depending on whether a number is being added or subtracted. For example, to subtract 2 from 7, start with 7 fingers raised, then lower 2 to be left with 5 fingers. Eventually, just looking at the number of fingers raised will make it clear how many fingers are raised, but for someone just starting, they can just count how many fingers are raised.