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**Definition 1.2.2.**An input-output system consists of a set of input trajectories [tex]\{u : T \rightarrow U\}[/tex] and output trajectories [tex]\{y : T \rightarrow Y \}[/tex] related by a mapping F. The system behaviour is given by [tex]\beta = \{(u, y) : T \rightarrow U \times Y ; y = F(u)\}[/tex]."

The parts of the quote in latex is what I don't understand. I can have a general idea what he means, but where do students learn this notation? Is it real analysis? If so, I can just buy a book and read since I've seen notation like this practically everywhere without explanation which leads me to think that it's rather elementary.