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.

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