halmazfelosztása

Halmazfelosztása, a Hungarian term, translates to "partition of a set" in English. In mathematics, a partition of a set is a division of the set into non-empty subsets such that every element of the set is included in exactly one of these subsets. Formally, if S is a set, then a partition of S is a collection of subsets P = {S1, S2, ..., Sn} such that the union of all subsets in P equals S, and the intersection of any two distinct subsets in P is empty. Additionally, each subset Si must be non-empty. The subsets that form the partition are called blocks or parts. For instance, if the set S is {1, 2, 3}, then {{1}, {2, 3}} is a partition of S. Another partition is {{1, 2, 3}}. However, {{1}, {2}} is not a partition because the element 3 is not included. Similarly, {{1, 2}, {2, 3}} is not a partition because the element 2 is in both subsets. The concept of set partitions is fundamental in combinatorics and abstract algebra, appearing in various contexts such as the study of equivalence relations and the classification of finite sets.