Where Can I Learn This Notation?

[Physics_wiz]

I'm trying to read a mathematical systems theory book (by Heij, Ran, and van Schagen) and he uses notation that I don't understand. He's not the only one...other books use the same notation too, but I never learned it. For example:

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

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.

 

[JasonRox]

I'm trying to read a mathematical systems theory book (by Heij, Ran, and van Schagen) and he uses notation that I don't understand. He's not the only one...other books use the same notation too, but I never learned it. For example:

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

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.

It's rather an elementary thing, which is a good thing!

I would say just read any decent Analysis, Topology or Set Theory introduction and you'll get it. Only like chapter 1 pretty much.

It might look weird now, but once you get it, you won't want to write any other way. It's the easiest way to write math ideas down.