For a preorder \((P, \leq)\), the meet and join of \(A \subseteq P\).
The meet \(\wedge A\) is an element such that
\(\forall a \in A: \wedge A \leq a\)
\(\forall q \in P: (\forall a \in A: q \leq a) \implies q \leq \wedge A\)
Think of as a GREATEST LOWER BOUND
The join \(\vee A\) is an element such that
\(\forall a \in A: a \leq \vee A\)
\(\forall q \in P: (\forall a \in A: a \leq q) \implies \vee A \leq q\)
Think of as a LEAST UPPER BOUND