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- Q6269005 subject Q7012223.
- Q6269005 subject Q7452041.
- Q6269005 subject Q8480477.
- Q6269005 abstract "In a partially ordered set P, the join and meet of a subset S are respectively the supremum (least upper bound) of S, denoted ⋁S, and infimum (greatest lower bound) of S, denoted ⋀S. In general, the join and meet of a subset of a partially ordered set need not exist; when they do exist, they are elements of P. Join and meet can also be defined as a commutative, associative and idempotent partial binary operation on pairs of elements from P. If a and b are elements from P, the join is denoted as a ∨ b and the meet is denoted a ∧ b. Join and meet are symmetric duals with respect to order inversion. The join/meet of a subset of a totally ordered set is simply its maximal/minimal element. A partially ordered set in which all pairs have a join is a join-semilattice. Dually, a partially ordered set in which all pairs have a meet is a meet-semilattice. A partially ordered set that is both a join-semilattice and a meet-semilattice is a lattice. A lattice in which every subset, not just every pair, possesses a meet and a join is a complete lattice. It is also possible to define a partial lattice, in which not all pairs have a meet or join but the operations (when defined) satisfy certain axioms.".
- Q6269005 thumbnail Join_and_meet.svg?width=300.
- Q6269005 wikiPageExternalLink books?id=SoGLVCPuOz0C&pg=PA52.
- Q6269005 wikiPageWikiLink Q130901.
- Q6269005 wikiPageWikiLink Q164307.
- Q6269005 wikiPageWikiLink Q165474.
- Q6269005 wikiPageWikiLink Q17502105.
- Q6269005 wikiPageWikiLink Q1756942.
- Q6269005 wikiPageWikiLink Q177251.
- Q6269005 wikiPageWikiLink Q177646.
- Q6269005 wikiPageWikiLink Q2362924.
- Q6269005 wikiPageWikiLink Q368988.
- Q6269005 wikiPageWikiLink Q369377.
- Q6269005 wikiPageWikiLink Q474715.
- Q6269005 wikiPageWikiLink Q5156540.
- Q6269005 wikiPageWikiLink Q554403.
- Q6269005 wikiPageWikiLink Q595364.
- Q6269005 wikiPageWikiLink Q6094393.
- Q6269005 wikiPageWikiLink Q7012223.
- Q6269005 wikiPageWikiLink Q7452041.
- Q6269005 wikiPageWikiLink Q834585.
- Q6269005 wikiPageWikiLink Q8480477.
- Q6269005 wikiPageWikiLink Q912887.
- Q6269005 comment "In a partially ordered set P, the join and meet of a subset S are respectively the supremum (least upper bound) of S, denoted ⋁S, and infimum (greatest lower bound) of S, denoted ⋀S. In general, the join and meet of a subset of a partially ordered set need not exist; when they do exist, they are elements of P. Join and meet can also be defined as a commutative, associative and idempotent partial binary operation on pairs of elements from P.".
- Q6269005 label "Join and meet".
- Q6269005 depiction Join_and_meet.svg.