Räknarbart

Räknarbart is a Swedish term used in mathematics, particularly in set theory. It translates to "countable" in English. A set is considered räknarbart if its elements can be put into a one-to-one correspondence with the natural numbers, or a subset of the natural numbers. This means that the elements of the set can be listed in an infinite sequence, without any element being left out.

There are two types of räknarbart sets: countably infinite and finite. A countably infinite set is a set that can be put into a one-to-one correspondence with the set of all natural numbers {1, 2, 3, ...}. Examples of countably infinite sets include the set of integers and the set of rational numbers. Despite appearing "larger" than the natural numbers, they can be shown to have the same cardinality, or size.

A finite set is also considered räknarbart, as its elements can be explicitly listed and counted. For instance, the set of days in a week is räknarbart because it contains only seven elements. The concept of countability is fundamental in understanding the different sizes of infinite sets, a field pioneered by Georg Cantor. Sets that are not räknarbart are called uncountable.