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.
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 5 and the cardinality is 5
Example #2
B = {☺,☺,☺}
1 → ☺
2 → ☺
3 → ☺
The cardinal numbers are 1, 2, 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!
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
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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