ækvivalensklasser
Ækvivalensklasser, also known as equivalence classes, are a fundamental concept in abstract algebra and set theory. An equivalence class is a subset of a larger set, where all elements within that subset share a common property defined by an equivalence relation. An equivalence relation is a binary relation that is reflexive, symmetric, and transitive.
Reflexivity means that every element in the set is related to itself. Symmetry implies that if element
When an equivalence relation is defined on a set, it partitions the set into disjoint equivalence classes.
For example, consider the set of integers and the relation "has the same remainder when divided by