Cardinal number

Definition · applies to numbers

Elementary

A cardinal number is a number that tells how many.

Graduate (set theory)

The cardinal number of a set is its cardinality. Two sets have the same cardinal number if there is a bijection between them.

Examples

Examples

• The “3” in “3 apples” Elementary
  The “3” in “3 apples” is a cardinal number because it tells how many apples there are.

Non-examples

Things that may be mistaken for examples.

• A phone number Elementary
• The “23” on a jersey Elementary
  The “23” on a jersey is not a cardinal number: it doesn’t count items in a set.
• The “3rd” in “finished 3rd” Elementary
  The “3rd” in “finished 3rd” is not a cardinal number, because it does not count the number of items in a collection.

Properties

• The cardinal numbers include the natural numbers and infinite cardinals, such as $\aleph_0$, the cardinality of $\nats$.

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