i'm studing the Probability Theory and i came to the concept of Event.
To me, it seems that an event can be represented as a set of sets, where every single element of the set represent a possible outcome of the event. For example,if i roll 2 dies and i want the event that at every roll each die has to be a value < 3, i can represent the event as:
$E=\left \{ \left \{ 1,1 \right \},\left \{ 1,2 \right \},\left \{ 2,1 \right \},\left \{ 2,2 \right \} \right \}$
Is it ok to represent an Event in this way, or other representations are better ?
It is better to represent $E=\{(1,1),(1,2),(2,1),(2,2)\}$ for the aforementioned reasons above, $\{1,2\}=\{2,1\}$ but $(1,2)\neq(2,1)$.