There are situations in Numerical Analysis concerning the convergence and properties of discretization procedures which seem to be of different type (e.g. convergence to genuine or to weak solutions, convergence to entropy solutions, creation of dicrete solutions which have to imitate properties of the seeked solutions known in advance etc.) but can uniformly be descibed by a property introduced here, called continuous convergence of relations. Historical examples demonstrate this standardization. (C) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.