"Completeness" of eigenvectors in a complete, commuting set Hi guys, I asked this question on Physics Stack Exchange many days ago and even after substantial discussions and revisions, this has remain unanswered. This is: http://physics.stackexchange.com/qu...igenvectors-in-a-complete-commuting-set/18272 It seems quite fundamental that I want to know what's actually going on. Is Dirac's generalization argument incomplete? Or is there a problem in my concepts of mathematics of ket spaces? The discussion on this can go on in this thread as it is usually discouraged on Stack Exchange. Hope to find substantial insight into it here.