Részrend

A részrend is a Hungarian term that translates to "partial order" in English. It describes a specific type of binary relation defined on a set. A relation R on a set A is a részrend if it satisfies three properties: reflexivity, antisymmetry, and transitivity.

Reflexivity means that every element in the set is related to itself. In mathematical terms, for any element 'a' in set 'A', the relation R holds between 'a' and 'a'. Antisymmetry implies that if two distinct elements are related to each other in both directions, then they must be the same element. Formally, if 'a' is related to 'b' and 'b' is related to 'a' by R, then 'a' must equal 'b'. Transitivity states that if an element 'a' is related to 'b' and 'b' is related to 'c', then 'a' must also be related to 'c'.

Examples of partial orders include the "less than or equal to" relation on the set of real numbers, or the "is a subset of" relation on the power set of a given set. In contrast, a "strict partial order" omits the reflexive property. Részrend are fundamental concepts in set theory and have applications in various fields such as computer science, discrete mathematics, and logic.