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
- The cardinality of a finite set is simply the count of its elements.
- Two sets have the same cardinality if there is a one-to-one correspondence between their elements.
- The symbol |A| denotes the cardinality of set A.
- Infinite sets can have different cardinalities; for instance, the set of natural numbers and real numbers have different infinite cardinalities.
- 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?
"Cardinality" appears in:
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.
