state space

A state space is the set of all possible states a given system may be at a particular moment in time.

EXAMPLE

For a die of six sides: $S=\{1,2,3,4,5,6\}$

For the weather (we could consider more states): $S=\{sunny,rainy,snowy\}$

We may have discrete (e.g. $\mathbb{N}$) or continuos (e.g. $\mathbb{R}$) state spaces. They may also be finite or infinite.

More on this topic later, as we can say many things about it in the domain of control theory or physics.