# Where Can I Learn This Notation?

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
Homework Helper
Gold Member
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.
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