halmazát

Halmazát is a Hungarian noun form derived from halmaz, meaning set. In general usage halmazát functions as a definite direct object with a third-person possessive nuance, translating roughly as “its set” or “the set’s” in English, depending on sentence context. The form reflects Hungarian’s rich system of suffixal morphology, where possession and definiteness interact with the object marker.

Halmaz, or halmazok in plural, is a fundamental concept in mathematics representing a collection of elements. An element either belongs to a set or does not. Sets are usually denoted by braces, for example {1, 2, 3}. The empty set is written ∅. Sets may be finite or infinite, and their size is called the cardinality, often written |A|. Subsets satisfy A ⊆ B, and equality of sets means they have exactly the same elements. Core operations include the union A ∪ B, the intersection A ∩ B, and the difference A \ B. The complement of a set A relative to a universal set U is U \ A. The power set P(A) is the set of all subsets of A. In formal contexts, sets underpin more advanced topics such as functions and relations.

In Hungarian mathematical prose, halmazát may appear when the set is the object of a verb and is marked as definite, often with examples like A halmazát megvizsgáltuk (We examined its set) or A halmazát határoztuk meg (We determine its set). The standard term for the object “set” remains halmaz, while halmazát is one inflected form used within proper grammatical constructions.