There are many definitions of what a system is, I like Mario Bunge’s definition:
“A system is a complex object every part or component of which is connected with other parts of the same object in such a manner that the whole possesses some features that its components lack – that is emergent properties” (Bunge 1996: 20).
Examples of emergent properties of a system: structure or history of social system. Examples of emergent properties of a component (i.e., part would not possess property if were independent or isolated): role, civil right, scarcity, price (Bunge 1996: 20).
quotes from: Bunge, Mario Augusto. Finding Philosophy in Social Science. New Haven and London: Yale University Press, 1996.
In my understanding of open systems, its components are continuously changing with their environment. Open systems have the emergent property of continuous exchange (input/output) of their components with the environment. Ludwig von Bertalanffy argues that open systems reach states of equilibrium within and through this interaction with their environment. Closed systems are isolated from their environment. Is mathematics a closed system?
[Photomedia Forum post by T.Neugebauer from Jan 10, 2007]