In addition to rays, a Hilbert space of dimension \(d\) also contains subspaces of dimension 2, 3, etc., up to \(d\) (the entire space). These larger subspaces also represent quantum properties and are the analogues of sets of more than one point in a classical phase space. Each subspace \(\PC\) corresponds to a unique projector \(P\), a Hermitian operator \(P=P^\dagger =P^2\) such that \(P\ket{\phi}=\ket{\phi}\) if and only if \(\ket{\phi}\) belongs to \(\PC\). A quantum projector behaves in many ways like a classical indicator function, e.g., its eigenvalues can only be 0 or 1. Using the same symbol \(P\) for the property and the projector should cause no confusion. Following Sec. III.5 of J. von Neumann (1932), we identify the negation \(\lnot P\) of a quantum property \(P\), subspace \(\PC\), with the orthogonal complement \(\PC^\perp\) consisting of the kets in \(\HC\) which are orthogonal to all the kets in \(\PC\). The projector on \(\PC^\perp\) is \(I-P\), again analogous to the classical case.