Hi. I have a question about numbers of basis in quamutum mechanics space. Hamiltonian of harmonic oscillator is observable and have countably infinite sets |En>s Together with position or momentum basis identity equation is, [tex]|state>=\int|x><x|state>dx=\int|p><p|state>dp=\Sigma_n\ |E_n><E_n|state>[/tex] The same state is expressed as both enumerable and denumerable infinite sets. Is it OK? Denumerable sets should be interpreted correctle as enumerable or vice versa?