What is a system?

A signal was defined as a mapping from a set of the independent variable (domain) to the set of the dependent variable (co-domain). A system is also a mapping, but across signals, or across mappings . That is, the domain set and the co-domain set for a system are both sets of signals, and corresponding to each signal in the domain set, there exists a unique signal in the co-domain set.

In signals and systems terminology, we say; corresponding to every possible input signal, a system “produces” an output signal.

In that sense, realize that a system, as a mapping is one step hierarchically higher than a signal. While the correspondence for a signal is from one element of one set to a unique element of another, the correspondence for a system is from one whole mapping from a set of mappings to a unique mapping in another set of mappings!