schwache

Schwache is the weak declension form of the German adjective schwach, meaning weak or frail. It is used for the singular forms when the adjective follows definite determiners, for example der schwache Mann, die schwache Frau, das schwache Kind. In the plural, the corresponding weak ending is -en: die schwachen Männer, die schwachen Kinder. The form schwache is also encountered in feminine singular after definite or demonstrative determiners in conventional phrasing, and in various fixed expressions.

Etymology and related forms: schwach derives from Old High German swach and is related to similar words in other Germanic languages, such as Dutch zwak and English weak. The adjective has a wide range of figurative and literal uses in modern German, from describing physical strength to moral or psychological states.

Usage and scope: In everyday language, schwache describes something lacking strength or vigor, as in physical weakness, weak performance, or weak signals. It also appears in figurative expressions, such as schwache Kräfte or schwache Argumente, to denote insufficiency or lack of impact. In academic and technical contexts, the word forms part of standard phrases like schwache Konvergenz (weak convergence) in functional analysis, schwache Lösung (weak solution) in partial differential equations, and schwache Form (weak form) of a problem. The noun form das Schwache (often plural die Schwachen) may be used in philosophical or social discussions to refer to a group of people considered weak or vulnerable.

See also: German grammar and declension patterns; semantics of weakness in language; mathematical terminology using schwache Konvergenz and related terms.