countrably

Countrably is a term used in mathematics, specifically within set theory, to describe a set that has the same cardinality as the set of natural numbers. Sets with this property are called countably infinite or denumerable. This means that the elements of the set can be put into a one-to-one correspondence with the natural numbers {1, 2, 3, ...}.

If a set is finite, it is considered countably infinite. For example, the set of even numbers {2, 4, 6, ...} is countably infinite because there is a bijection between the natural numbers and the even numbers (e.g., mapping n to 2n). The set of all integers is also countably infinite, as is the set of all rational numbers.

The concept of countability is fundamental to understanding different sizes of infinity. While the set of natural numbers, integers, and rational numbers are all countable, the set of real numbers is not. Sets that are not countable are referred to as uncountable. Georg Cantor introduced the formal definition of countability and demonstrated the existence of different sizes of infinity.