Epäparien

Epäparien is the genitive plural form of the Finnish noun epäpari, a term used to refer to elements that do not form a pair. In mathematical and related texts, epäpari is often used to denote elements that stand outside a matching or pairing scheme, and by extension epäparien means “of the unpaired elements” or “the odd items.”

Usage and terminology vary. In standard Finnish, the more common term for numbers that are not divisible by two is pariton luku (odd number). Epäpari is encountered in some mathematical writings, combinatorics, and older or more technical contexts, where the focus is on unpaired or non-paired items rather than on a formal parity concept. The form epäparien appears in phrases describing counts or sets of such elements, for example epäparien lukumäärä (the number of unpaired/odd elements) or epäparien joukko (the set of odd elements).

In number theory, epäparien typically correspond to odd integers, such as 1, 3, 5, and so on. A basic property is that the sum of two epäparien is even, while the product of two epäparien is odd. In pairing problems, epäparien can refer to items left over after maximal pairing; for n items with p pairs formed, the number of epäparien is n − 2p.

Etymology-wise, epäparien is the genitive plural form of epäpari, built from epä- (not) + pari (pair). Related concepts include parity and odd numbers.