Subset of a set

According to set theory, the concept of a subset from a set – applies to a certain part of a set. A subset exists if every element of it belongs to another larger or equal set.

Among subsets, one can separately distinguish the proper and the empty non-trivial subset, which is the smallest set. The relation of subsets is characterized by properties of reflexivity, transitivity, antisymmetry, etc.

When assessing the quantitative characteristics of subsets of finite element sets, a binomial coefficient is used. The concept of subsets from sets is applied for practical purposes in solving analytical problems in statistics, set algebra, probability theory, and in various directions of applied mathematics.