Numeroituvasti

Numeroituvasti is a Finnish term that translates to "countably" in English. It is primarily used in mathematics, particularly in set theory, to describe sets that can be put into a one-to-one correspondence with the set of natural numbers. This means that the elements of a countably infinite set can be listed in an ordered sequence, even though the sequence is infinite.

A set is considered numeroituvasti infinite if there exists a bijective function between the set and the set of natural numbers {1, 2, 3, ...}. This implies that even though the set has infinitely many elements, each element can be assigned a unique natural number. Examples of numeroituvasti infinite sets include the set of integers and the set of rational numbers.

Finite sets are also considered numeroituvasti, as their elements can be easily counted and listed. The term thus encompasses both finite and countably infinite sets. Sets that are not numeroituvasti are called uncountably infinite, meaning their elements cannot be put into such a one-to-one correspondence with the natural numbers. The set of real numbers is a well-known example of an uncountably infinite set. The concept of numeroituvasti is fundamental for understanding different sizes of infinity in mathematics.