High Quality Content by WIKIPEDIA articles! In mathematics, a join-semilattice is a partially ordered set which has a join (a least upper bound) for any nonempty finite subset. Dually, a meet-semilattice is a partially ordered set which has a meet (or greatest lower bound) for any nonempty finite subset. Every join-semilattice is a meet-semilattice in the inverse order and vice versa. Semilattices can also be defined algebraically: join and meet are associative, commutative, idempotent binary operations, and any such operation induces a partial order (and the respective inverse order) such that the result of the operation for any two elements is the least upper bound (or greatest lower bound) of the elements with respect to this partial order.

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