ikkenumrerbare

Ikkenumrerbare is a term used in Norwegian mathematical discourse to describe a set or collection that cannot be enumerated by a list indexed by natural numbers. In standard mathematical terminology, such sets are called uncountable.

A set is typically classified as finite (and therefore enumerable), countably infinite (there exists a bijection with the natural numbers), or uncountable (no such bijection exists). Thus, ikkenumrerbare describes a property of sets that are not in one-to-one correspondence with the natural numbers.

Common examples of ikkenumrerbare sets are uncountable, such as the real numbers within an interval like [0, 1], a fact established by Cantor’s diagonal argument. It follows that the set of all real numbers, the set of irrational numbers, and the power set of natural numbers are uncountable. In contrast, the rationals, integers, and natural numbers are countable (finite or countably infinite).

Uncountability is a central concept in set theory with implications for measure and topology, highlighting the existence of different infinities and cardinalities. Related ideas include Cantor’s theorem, the continuum, and the continuum hypothesis. In Norwegian mathematical usage, ikkenumrerbare functions as the translation or equivalent of the English term unclecountable, signaling non-enumerability.