In mathematics, a set is considered "countable" if its elements can be matched one-to-one with the natural numbers 1, 2, 3, .... This means that you can list the elements in a sequence, even if the list goes on forever. For example, the set of all integers is countable because you can arrange them in a sequence like 0, 1, -1, 2, -2, .... Countable sets can be finite or infinite. A finite set, like the fruits in a basket, has a limited number of elements, while an infinite set, such as the even numbers, continues indefinitely. Understanding countable sets helps in various fields, including computer science and statistics, where organizing data is essential.