In this selection from the Web Dictionary of Cybernetics and Systems, a system is defined as:

(1) A set of variables selected by an observer (Ashby) together with the constraints across variables he either discovers, hypothesises or prefers. Inasmuch as the variables of a system may represent (see representation) the components of a complex machine, an organism or a social institution and a constraint is the logical complement of a relation,an equivalent definition of system is that (2) it represents a set of components together with the relations connecting them to form a whole unity.

http://pespmc1.vub.ac.be/ASC/SYSTEM.html

In my opinion, the term system implies and carries more complexity than the word set. Set is a term or a discrete arrangement of matter or energy that can be described in terms of the elements that comprise it. A system describes the existence of elements in a set, how those elements are related, and also the behavior of those elements (or specific subsets of those elements) over an interal of time. The word system implies that the relationships among the elements of a set of information are in state of change over an interval of time, or that a subset of information contained in a system may be subject to processes of change. While the process of observation may make a person aware of an existing system, observation is not necessary for a system to exist.

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