arbitrær

Arbitrær is a Norwegian adjective meaning arbitrary or chosen without a specific reason, beyond the constraints stated in a problem or situation. In everyday language it often describes a choice that is not guided by necessity or a fixed rule, and may be any option within a given set. In formal contexts, such as mathematics and logic, arbitrær has a more precise use: it denotes a value or element that is selected freely from a domain, with no additional restrictions beyond those already specified.

In mathematics and logic, the term is used to generalize statements. For example, letting x be an arbitrær value in a set means that the statement should hold for any possible choice of x within that set. This allows proofs to address a generic case rather than a particular instance. Phrases like for arbitrære x or la x være en arbitrær verdi are common in textbooks and proofs. The concept helps distinguish universal claims from specific examples.

It is important to distinguish arbitrær from tilfeldig (random). An arbitrær choice is not necessarily random or probabilistic; it is chosen to demonstrate generality or to satisfy given constraints. The concept is often employed in defining arbitrære konstanter (arbitrary constants) or arbitrære funksjoner (arbitrary functions) in definitions, proofs, and theoretical discussions.

Etymologically, arbitrær stems from Latin arbitarius, via French arbitraire, related to judging or deciding. In Norwegian usage, the term remains tied to the idea of selection by reasoned choice within a defined framework rather than by chance.