halmazának

Halmazának is a Hungarian term formed from the noun halmaz, meaning set, with the possessive suffix -ának. It serves to denote that something belongs to or is related to a particular set, and it corresponds to the English possessive phrase “the set’s” or “of the set.” The form is typically used with third-person singular possessors, and appears in phrases such as halmazának elemei (the elements of the set) or halmazának határai (the boundaries of the set).

In mathematical language, a halmaz (set) is a well-defined collection of distinct objects, called elements, for which membership is determined by a relation written with the symbol ∈. A set is characterized by its elements, and its properties are explored through notions such as subset, intersection, union, and cardinality. The construction halmazának elemei simply relocates attention to the elements belonging to a given set; for example, if A = {1, 2, 3}, then halmazának elemei are 1, 2 and 3.

Grammatically, halmazának can also appear in contexts that indicate possession or association with the set being described, such as halmazának elemszáma (the cardinality of the set) or halmazának tulajdonságai (the properties of the set). It is part of the broader Hungarian system of suffix-based possession, where the form changes to reflect different possessors and cases.

Overall, halmazának functions as a linguistic tool to attribute attributes or contents to a specific set within mathematical discourse.