A partition of a set is a grouping of its elements into non-empty subsets such that every element belongs to exactly one subset. Every equivalence relation on a set defines a partition of that set, and every partition in turn defines an equivalence relation, so the two notions are interchangeable. A set equipped with an equivalence relation or a partition is sometimes called a setoid, a term used mainly in type theory and proof theory.
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1. Set Theory (Wikipedia)
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Around 1871, influenced by Riemann, Dedekind began working with sets in his publications, which dealt very clearly and precisely with equivalence relations, partitions of sets, and homomorphisms.
Partition of a Set (Wikipedia)
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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.
Associated With: Sets, Lead section, first sentence
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
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