Join and meet

Summary

In a partially ordered set, the join of two elements is their least upper bound and the meet is their greatest lower bound. They are written $x \vee y$ and $x \wedge y$. Join and meet are the supremum and the infimum of a two-element set, seen as binary operations. They are the basic operations of lattice theory: a poset in which all joins and meets of pairs exist is a lattice.