 Discreteness appears in two related ways in quantum theory. First, the amount of information that can be gathered regarding the state of a system which is in a finite region R of its phase space is finite. It is given by the Liouville measure of R divided by the Planck constant, per degree of freedom. This is what causes discrete spectra. Continuous spectra require infinite phase spaces, and can be seen as effects of idealisations. The discreteness of quantum mechanics is captured by the first of the two informational postulates.