dowolna

Dowolna is the feminine singular form of the Polish adjective dowolny, meaning arbitrary or any. It is used to indicate that a thing is not fixed and may be chosen freely from a set. The form dowolna modifies feminine nouns, for example dowolna liczba (any number), dowolna osoba (any person), or dowolna funkcja (an arbitrary function). The corresponding masculine and neuter forms are dowolny and dowolne.

In mathematical or logical contexts, dowolna denotes that a statement holds for an arbitrary element of a set, without specifying which one. Phrases include dla dowolnej liczby rzeczywistej x (for any real number x) and dla dowolnej wartości parametru (for an arbitrary parameter value). In programming or instruction manuals, it is used similarly: Podaj dowolne hasło (provide any password), Wybierz dowolne miejsce (choose any location).

Difference from related terms: dowolny contrasts with losowy (random) in that dowolny means allowed for selection without implying randomness; the selection can be intentional or user-specified, whereas losowy implies a random outcome. The noun dowolność expresses arbitrariness or freedom of choice, and the adverb dowolnie means arbitrarily or freely.

Overall, dowolna functions as a linguistic tool to express non-specificity with feminine nouns, commonly encountered in mathematics, logic, and technical writing.