 Let’s examine this “logical calculus” of projections. Ordered by set-inclusion, the closed subspaces of \(\mathbf{H}\) form a complete lattice, in which the meet (greatest lower bound) of a set of subspaces is their intersection, while their join (least upper bound) is the closed span of their union. Since a typical closed subspace has infinitely many complementary closed subspaces, this lattice is not distributive; however, it is orthocomplemented by the mapping 