räknelig

Räknelig is a Swedish word that translates to countable in English. It is primarily used in linguistics and mathematics to describe sets or nouns that can be enumerated. In grammar, räknelig refers to nouns that can be counted individually and typically have both singular and plural forms. For example, "bok" (book) is a räknelig noun, as it can be counted as one book, two books, etc. Conversely, "mjölk" (milk) is an iräknelig (uncountable) noun, as it cannot be counted as individual units.

In mathematics, the concept of räknelig applies to sets. A set is considered räknelig if its elements can be put into a one-to-one correspondence with the natural numbers. This means that the elements can be listed in an infinite sequence, even if the set is infinite. The set of natural numbers itself is the prime example of a räknelig set. The set of integers and the set of rational numbers are also räknelig. Sets that are not räknelig are called överräknelig (uncountable), meaning they have a larger cardinality than the natural numbers. The set of real numbers is a classic example of an överräknelig set. The distinction between räknelig and överräknelig is fundamental in set theory and analysis.