Countability refers to the ability to determine whether a set can be matched one-to-one with the set of natural numbers, 0, 1, 2, .... A set is considered countable if its elements can be listed in a sequence, even if the list is infinite. Examples of countable sets include the set of integers and the set of rational numbers. In contrast, uncountable sets cannot be matched with natural numbers. The most famous example of an uncountable set is the set of real numbers, which includes all rational and irrational numbers. This distinction is important in mathematics, particularly in set theory and infinity studies.