Oändlighetsper

Oändlighetsper is a coined term in Swedish-language discussions of mathematics and philosophy that refers to a hypothetical measure describing a quantity per infinity. It is not a standard or widely used mathematical object, and its precise meaning can vary depending on the context in which it is introduced. In general, the term is used to provoke thought about how quantities behave when compared to or scaled by an infinite quantity.

Etymology and origin: The word combines oändlighet, meaning infinity, with per, meaning per or for each. Because it is a neologism rather than a conventional concept, oändlighetsper has appeared mainly in informal writings, teaching analogies, and some science-fiction narratives to illustrate ideas about scaling, limits, or densities in the limit. In formal discussions, scholars will typically replace it with established notions such as limits, densities, or asymptotic ratios, unless a specific text defines it explicitly.

Formalization and examples: Since oändlighetsper is not standardized, any formalization depends on the author. A common illustrative approach is to define oändlighetsper(f,g) as a limit of the ratio f(n)/g(n) as n tends to infinity, when the limit exists. This is only a pedagogical device to discuss how a quantity grows relative to an infinite benchmark, not a universal definition. In educational contexts, it may serve as a heuristic to contrast finite measurements with infinite scales or to discuss the idea that some effects vanish or persist when faced with infinity.

Usage and reception: The term is primarily of interest in teaching, thought experiments, or speculative writing rather than in formal mathematical practice. When used, it should be clearly defined within the work to avoid ambiguity.

See also: infinity, limit, asymptotics, density, infinitesimal.