quotiëntverzamelingen
Quotient sets, also known as quotient spaces or factor sets, are a fundamental concept in mathematics, particularly in set theory and abstract algebra. A quotient set is formed by partitioning a given set into equivalence classes based on an equivalence relation. An equivalence relation is a binary relation that is reflexive, symmetric, and transitive. When an equivalence relation is defined on a set, it divides the set into disjoint subsets, where each subset contains elements that are equivalent to each other. These subsets are precisely the equivalence classes. The quotient set is then the set of all these distinct equivalence classes.
For example, consider the set of integers and the equivalence relation "congruence modulo n". Two integers are