In general the filling factor ν ν is not an integer. It happens to be an integer when there is an exact number of filled Landau levels. Instead, it becomes a non-integer when the top level is not fully occupied. In actual experiments, one varies the magnetic field and fixes electron density (and not the Fermi energy!) or varies the electron density and fixes the magnetic field. Both cases correspond to a continuous variation of the filling factor ν ν and one cannot expect ν ν to be an integer. Since n B ∝ ∝ B , by increasing the magnetic field, the Landau levels move up in energy and the number of states in each level grow, so fewer electrons occupy the top level until it becomes empty. If the magnetic field keeps increasing, eventually, all electrons will be in the lowest Landau level ( ν ν < 1 ) and this is called the magnetic quantum limit.