Countable infinity refers to a type of infinity that can be matched one-to-one with the set of natural numbers, 0, 1, 2, 3, .... This means that even though the set is infinite, its elements can be listed in a sequence. Examples of countably infinite sets include the set of integers and the set of rational numbers. In contrast to uncountable infinity, which cannot be listed in this way, countable infinity allows for a clear understanding of size and comparison. The concept is essential in mathematics, particularly in set theory, where it helps to categorize different types of infinities and their properties.