Numërueshme

Numërueshme is an Albanian word that translates to "countable" in English. It is primarily used in mathematics and set theory to describe sets whose elements can be put into a one-to-one correspondence with the natural numbers. This means that the elements of a numërueshme set can be listed out in an infinite sequence, even though the set itself is infinite.

A set is considered numërueshme if it is finite or countably infinite. Finite sets are those with a specific, limited number of elements, which are inherently countable. Countably infinite sets, on the other hand, are infinite but still possess a structure that allows for their elements to be enumerated. Examples of numërueshme sets include the set of natural numbers itself, the set of integers, and the set of rational numbers.

The concept of numërueshme is crucial in understanding different sizes of infinity. While all numërueshme sets have the same cardinality (the size of the set), there exist sets that are not numërueshme, meaning they are uncountably infinite and have a larger cardinality. The set of real numbers is a well-known example of an uncountable set. Understanding this distinction is fundamental in advanced mathematical fields.