Concept
Partition of a set
Overview
In mathematics, a partition of a set is a grouping of its elements into non-empty subsets, in such a way that every element is included in exactly one subset.
Every equivalence relation on a set defines a partition of this set, and every partition defines an equivalence relation. A set equipped with an equivalence relation or a partition is sometimes called a setoid, typically in type theory and proof theory.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Related ideas
- Proof theory
- Mathematics
- Intersection (set theory)
- Recursion
- Set (mathematics)
- Subset
- Singleton (mathematics)
- Type theory
- Union (set theory)
- Complement (set theory)
- Axiom of choice
- Equivalence relation
- Empty set
Place in the tradition
Part of Outline of logic.