A distributed dynamic system is a fully distributed system subject to a continual arrival/departure of the entities defining the system. Another characterizing dimension of these systems is their, possibly, arbitrary large size (number of entities) and the possible arbitrary small part of the system a single entity directly interacts with. This interaction occurs through data exchange over logical links, and the constantly changing graph, formed by all links connecting entities, represents the overlay network of the dynamic distributed system. The connectivity of such overlay is of fundamental importance to make the whole system working. This paper gives a precise definition of the connectivity problem in dynamic distributed systems while formally defining assumptions on arrival/departure of entities and on the evolution of the system size along the time. The paper shows the impossibility of achieving connectivity when an arbitrary large number of entities may arrive/depart concurre...