numeroitavissa

Numeroitavissa is a Finnish mathematical term meaning “countable” or “enumerable.” It describes a set that can be put into a one-to-one correspondence with the natural numbers. More formally, a set S is numeroitavissa if there exists a bijection f: N -> S. From this definition follows that a numeroitavissa joukko on joko äärellinen tai numeroitavan ääretön. Finite sets are trivially numeroitavissa, since they can be matched with a finite initial segment of N. An infinite numeroitavissa set can be listed in a sequence, even though the listing continues without end.

Examples and non-examples are central to understanding the concept. The set of natural numbers N, the set of integers Z, and the set of rational numbers Q are numeroitavissa. In each case there exists an explicit bijection with N (for Z and Q, standard enumerations show the correspondence). The real numbers R, however, are not numeroitavissa; Cantor’s diagonal argument demonstrates that no bijection exists between N and R, so R is uncountable.

In a broader context, numeroitavissa is tied to the study of cardinality and the distinction between finite, countably infinite, and uncountable sets. The property is sometimes summarized by saying that a numeroitavissa set can be numbered or listed in a sequence indexed by natural numbers. The concept contrasts with non-numberable (uncountable) sets, which cannot be arranged in such a sequence.