laskemattomat

Laskemattomat is a Finnish term meaning uncountable or innumerable. In mathematics, laskematon describes a set that cannot be put into a one-to-one correspondence with the natural numbers, and therefore is not countable. The opposite concept is laskettava, i.e., a countable set. A canonical example is the set of real numbers, which is uncountable; Cantor’s diagonal argument shows there is no bijection between the natural numbers and the reals. By contrast, the sets of natural numbers, integers, and rational numbers are countable, even though rationals are dense in the real numbers.

The notion extends to cardinalities: uncountable sets have cardinalities strictly greater than aleph-null, with the real numbers having cardinality often denoted as continuum c = 2^{aleph0}. In everyday Finnish, laskemattomat can also be used outside formal mathematics to mean “too many to count” or “innumerable,” as in laskemattomat mahdollisuudet (countless possibilities).

The term appears in educational materials on set theory, probability, and philosophy, and it is used to express the idea of limits to enumeration and the existence of infinite sizes that exceed countable infinity.