Ordinaler

Ordinaler is a term used in some languages, notably Swedish and Norwegian, as the plural of ordinal, referring to ordinal numbers—the adjectives or numerals that express a position in a sequential order (first, second, third, etc.). In English, the corresponding term is ordinals; the form ordinaler appears primarily in Scandinavian linguistic contexts.

In mathematics, ordinals (the general term for ordinal numbers) are a generalization of natural numbers that describe order types of well-ordered sets. Finite ordinals correspond to natural numbers 0, 1, 2, ..., while infinite ordinals such as ω extend the concept into the transfinite. Ordinals are well-ordered by less-than and are closed under the successor operation; many operations on ordinals (addition, multiplication, exponentiation) are not commutative, and limit ordinals are limits of increasing sequences.

In linguistics, ordinal forms often derive from cardinal numerals and are used to modify nouns or function as determiners, sometimes requiring agreement in gender, number, or case depending on the language.

Etymology: The term ordinal derives from Latin ordinalis, related to ordo “order.” The plural form ordinaler follows patterns in Scandinavian languages, where many nouns and loanwords take -er to form plurals or distinct noun forms.

See also: ordinal numbers, ordinals (set theory), linguistic ordinals, cardinal numbers.