Cardinality

Definition

Cardinality is the measure of the "number of elements" in a set. It helps compare the size of sets, even if they are infinite.

5 Must Know Facts For Your Next Test

1. The cardinality of a finite set is simply the count of its elements.
2. Two sets have the same cardinality if there is a one-to-one correspondence between their elements.
3. The symbol |A| denotes the cardinality of set A.
4. Infinite sets can have different cardinalities; for instance, the set of natural numbers and real numbers have different infinite cardinalities.
5. Aleph-null (ℵ₀) represents the smallest infinity, which is the cardinality of the set of natural numbers.

Review Questions

• What does it mean for two sets to have the same cardinality?
• How do you denote the cardinality of a set A?
• What is Aleph-null (ℵ₀) and what does it represent?

Related terms

Set: A collection of distinct objects, considered as an object in its own right.

One-to-One Correspondence: A situation where each element in one set pairs with exactly one element in another set, and vice versa.

Infinite Set: A set that has an unending number of elements.