What is a Cardinal Number? Definition and Examples


What is a cardinal number? A cardinal number is a natural number that is used in order to measure the size of sets or the number of items that are in a group. The number of items in the set or group is called cardinality.

Examples showing how to use cardinal numbers to find the cardinality of a set


Example #1

A = {-5, -4, -1, 2, 6}

The first 5 natural numbers are used to count the items in this set. 

1 → -5

2 → -4

3 → -1

4 →  2

5 →  6

The cardinal numbers are 1, 2, 3, 4, and and the cardinality is 5

Example #2

B = {,,}

1 → 

2 → 

3 → 

The cardinal numbers are 12, and 3 and the cardinality is 3

Example #3

C = {0}

1 → 0

The cardinal number is 1 and the cardinality is 1

Notice that 1 is the smallest cardinal number! 

What is the cardinality of the empty set?


The empty set is represented with {} or ø

Since the empty set has no elements, we cannot use any cardinal number(s) in order to count. The cardinality is 0

Is zero a cardinal number?


When we start counting, we always start with one, not zero as demonstrated in the examples above. Therefore, 0 is not a cardinal number because we do not use it to count the number of items in a set.

Recent math words

  1. What is an abacus? Definition and Chinese Abacus

    Jan 18, 22 08:00 AM

    What is an abacus? Learn quickly and easily to use an abacus to do math.

    Read More

  2. Width of an Object

    Jan 17, 22 09:15 AM

    What is the width of an object? Definition, explanation, and easy to understand real life examples.

    Read More

Enjoy this page? Please pay it forward. Here's how...

Would you prefer to share this page with others by linking to it?

  1. Click on the HTML link code below.
  2. Copy and paste it, adding a note of your own, into your blog, a Web page, forums, a blog comment, your Facebook account, or anywhere that someone would find this page valuable.
Share this page: