likelösningarnas

Likelösningarnas is a Swedish possessive form used to refer to the equal or identical solutions of mathematical problems, typically in plural. The base noun is likelösningar, formed from lika or lika värde (same, equal) and lösningar (solutions or answers). The definite plural is likelösningarna, and adding the -s suffix yields likelösningarnas, meaning “the equal solutions’” or “of the equal solutions.”

In mathematical context, likelösningarna describes the set of solutions that satisfy more than one equation or condition and are identical across the considered problems. The concept is especially relevant when comparing systems of equations, where two or more equations define the same solution set. If two equations are proportional or equivalent, they share the same likelösningarna, and any discussion of their properties often refers to this common solution set.

Usage examples in Swedish texts might discuss the properties of likelösningarna, such as their dimension, structure, or stability under transformations. For instance, in linear algebra a pair of equations whose left-hand sides are proportional will have identical likelösningar, illustrating equivalence of the systems.

Notes on grammar: likelösningarnas is formed from likelösningar in definite plural (likelösningarna) plus the genitive -s, a standard Swedish pattern for possessive forms. The singular possessive would be likelösningens (the equal solution’s). The term is primarily used in mathematical discourse, though it may appear in explanations or glossaries when discussing solution sets.