äärellisiä

äärellisiä is the plural partitive form of the Finnish adjective äärellinen, meaning finite, bounded, or having a limited size or number. The term is used in mathematics, computer science, and everyday language to describe objects or collections that contain only a finite number of elements, as opposed to infinite (ääretön). In Finnish, äärellistä and äärellisiä are used when the noun they modify is in the partitive case, for example äärellisiä arvoja (finite values) or äärellisiä joukkoja (finite sets).

In mathematical contexts, äärellinen is used to classify structures such as finite sets, finite sequences, and finite automata. A finite set has a limited cardinality, a finite sequence has a finite number of terms, and a finite automaton operates with a finite number of states. The concept also appears in analysis and combinatorics when finiteness conditions are required or stated.

Usage notes include the contrast with infinite (ääretön). Finns commonly say esimerkiksi: Joukko A on äärellinen, jos A sisältää rajatun määrän elementtejä, tai Jono on äärellinen, jos sen termien lukumäärä on rajoitettu. The termgars are used across formal and informal contexts, with äärellinen denoting a strict sense of finiteness, while more general phrases may use words like rajoitettu (restricted) to describe boundedness in a looser sense.