information:filtering
Meets of general subsets

If (A, ∧) {\displaystyle (A,\wedge)} is a meet-semilattice, then the meet may be extended to a well-defined meet of any non-empty finite set, by the technique described in iterated binary operations. Alternatively, if the meet defines or is defined by a partial order, some subsets of A {\displaystyle A} indeed have infima with respect to this, and it is reasonable to consider such an infimum as the meet of the subset. For non-empty finite subsets, the two approaches yield the same result, and so either may be taken as a definition of meet. In the case where each subset of A {\displaystyle A} has a meet, in fact (A, ≤) {\displaystyle (A,\leq)} is a complete lattice; for details, see completeness (order theory).