The connection between the continuousness of Rabi oscillation and the discontinuity of quantum jumps has long remained one of the conceptual difficulties since the discovery of the quantum physical paradigm. In this study, however, we demonstrate that the behavior of the atom-field composite system gradually changes from the continuous Rabi interaction to the discontinuous quantum jumps as the atom-field coupling strength is reduced. The reduction occurs through enlarging the quantization volume of the mode so that the mode approaches one of the infinitely many modes of the thermal background.