endlich

Endlich is a German word with multiple functions. As an adverb, it means "finally" or "at last," used to mark the conclusion of a period of waiting, effort, or anticipation. It can convey relief, satisfaction, or the sense that something long-awaited has occurred. In spoken language, it can stand alone as an interjection: "Endlich!"

In mathematics and other technical contexts, the term exists as an adjective meaning "finite," typically in phrases such as "endliche Menge" (finite set) or "endliche Folge" (finite sequence). This usage contrasts with "unendlich," which means infinite. The form of the adjective changes according to case, gender, and number, for example "endliche Mengen" or "eine endliche Lösung."

Etymology: the word is related to Ende (end) and expresses the sense of reaching an end or conclusion; it has developed from the idea of something coming to an end after a period.

Usage notes: besides its primary adverbial meaning, "endlich" is employed in various idioms and fixed expressions in everyday German, often with emphasis or emotional nuance. Its scope includes written and spoken language, including journalism, literature, and academic writing when referring to finiteness in a technical sense.

Related terms include Endlichkeit (finiteness) and Unendlichkeit (infinity), as well as Ende (end). The distinction between "endlich" as finite vs. "unendlich" as infinite is important in German mathematics and philosophy.