Överräknelig

"Överräknelig" is a Swedish term that translates to "countable" or "denumerable" in English, particularly in the context of set theory and mathematics. It refers to sets whose elements can be put into a one-to-one correspondence with the natural numbers (0, 1, 2, 3, ...).

A set is considered "överräknelig" if it is finite or countably infinite. Finite sets are those with a specific, limited number of elements, such as the set of days in a week. Countably infinite sets, while having an infinite number of elements, still possess the property that their elements can be listed in an unending sequence. Examples of countably infinite sets include the set of all integers (..., -2, -1, 0, 1, 2, ...) and the set of all rational numbers (numbers that can be expressed as a fraction p/q, where p and q are integers and q is not zero).

The concept of "överräknelig" is crucial for understanding different sizes of infinity. While some infinite sets are "överräknelig", others are not. Sets that are not "överräknelig" are called "underäknelig" or uncountable, meaning their elements cannot be put into a one-to-one correspondence with the natural numbers. A classic example of an uncountable set is the set of real numbers. The distinction between countable and uncountable infinities was a significant development in mathematics, primarily attributed to the work of Georg Cantor.