dénombrables

In mathematics, the term "dénombrables" refers to countably infinite sets. A set is considered countably infinite if its elements can be put into a one-to-one correspondence with the set of natural numbers (1, 2, 3, ...). This means that even though the set is infinite, its elements can be listed in an ordered sequence, and each element will eventually appear in that list.

The set of natural numbers itself is the archetypal example of a countably infinite set. Other examples include the set of integers (..., -2, -1, 0, 1, 2, ...), which can be listed as 0, 1, -1, 2, -2, and so on. The set of rational numbers (fractions) is also countably infinite. Despite appearing to be "denser" than integers, they can be systematically enumerated using methods like Cantor's diagonal argument or by ordering them based on the sum of their numerator and denominator.

The concept of countability is fundamental in set theory and has significant implications in areas like computability theory and the study of infinite sets. Sets that are not countably infinite are called uncountable. The set of real numbers is a prime example of an uncountable set.