Infinite matrices may violate the associative law

The momentum operator for a particle in a box is represented by an infinite order Hermitian matrix P . Its square P 2 is well defined (and diagonal), but its cube P 3 is ill defined, because P P 2 6= P 2 P . Truncating these matrices to a finite order restores the associative law, but leads to other curious results. Classification 0260 (02.10.Sp)