beliebigem

Beliebigem is the dative singular form of the German adjective and pronoun "beliebig," meaning "any," "arbitrary," or "as one pleases." Grammatically, "beliebigem" appears for masculine and neuter nouns in the dative case when the adjective follows strong declension patterns (often without a preceding article) or in certain pronominal uses. It commonly occurs after prepositions that govern the dative case, such as mit, bei, zu or nach.

Usage examples include phrases like "mit beliebigem Inhalt" (with any content), "bei beliebigem Wetter" (in any weather) and "in beliebigem Maße" (to any extent). In technical and formal contexts—for example mathematics, logic, and computer science—equivalent expressions signal universality or arbitrariness, though nominative or accusative forms (beliebiges, beliebiger, beliebige) are more frequent in statements like "für beliebiges x gilt..." (for any x it holds that...).

Etymologically, "beliebig" derives from the verb "belieben" (to please, be one's pleasure) combined with the adjectival suffix -ig, conveying the sense of something chosen freely or at will. In contemporary German it is neutral in register and widely used in both everyday and specialized language to express the notion of indifference among alternatives or generality.