Join (mathematics)

In mathematics, a join on a set is defined either as unique suprema (least upper bounds) with respect to a partial order on the set, provided such suprema exist, or (abstractly) as a commutative and associative binary operation satisfying an idempotency law. In either case, the set together with the join is a join-semilattice. The two definitions yield equivalent results, except that in the partial order approach it may be possible directly to define joins of more general sets of elements. The most common context in which to find a join is as one of the operations in a lattice.
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