lösbares

Lösbares is a German term used to designate something that can be solved. Grammatically, lösbares is the neuter singular form of the participle lö­sbar used as an adjective; the noun form das Lösbare is also used to refer to a solvable object, especially a problem, task or equation.

In mathematics and related fields, the concept of solvability describes whether an instance admits a solution or a method to compute it. For equations, lö­sbar can indicate that solutions exist and can be found, or that a particular form of solution is available (for example, lösbar durch Radikale, solvable by radicals). In algebra, a central use is lö­sbare Gruppen (solvable groups), which are groups with a subnormal series whose successive quotients are abelian; such groups are key in Galois theory and the study of solvability by radicals.

In everyday language, das Lösbare can be used to indicate that a task has a solution, as in ein lösbares Problem. The related noun Lösbarkeit denotes the property of being solvable, while Lösung refers to the actual solution. The term hårdly appears in contexts outside mathematics, where lösbar simply means capable of being solved, such as a puzzle or a practical problem.

See also: Lösbarkeit, Lösungsweg, Gleichung, Gruppe, Lösbarkeit durch Radikale.