halmazba

Halmazba is a Hungarian grammatical form derived from halmaz (set) with the directional suffix -ba. It is used in mathematical language to indicate movement into a set or, more commonly, membership in a set. The phrase is often paired with verbs such as tartozik (belongs) or kerül (enters) to express that an object becomes a member of a given set. In practice, halmazba conveys the same idea as the mathematical symbol x ∈ A, read "x belongs to A".

Halmazba contrasts with halmazban or halmazban/ben, which describe the location inside the set rather than movement into it. For example, "az 2 a halmazba tartozik" (2 belongs to the set) vs "az 2 a halmazban van" (2 is in the set).

Usage examples: "Az 3 az A halmazba tartozik." "Az x az A halmazba kerül." "Az 5 nem tartozik az A halmazba." In mathematical notation these correspond to 3 ∈ A, x ∈ A, and 5 ∉ A, respectively, depending on context.

Notes: In formal writing, authors often prefer other expressions such as "az A halmaz eleme" for "the element of A" or the symbol x ∈ A. The Hungarian phrase halmazba is part of everyday mathematical language rather than a separate mathematical symbol. It helps link natural language statements about membership to the formal concept of set theory.

See also: halmaz, halmazelmélet, elem, tartozik, halmazhoz tartozás.