I am going through a lecture on Turing Machines and am confused by the use of notations for the transition state function.
The transition function is defined as $$ Q\times\sum \rightarrow (\sum \cup \{ L,R\}) \times Q$$
Where Q is the set of states, $\sum$= tape alphabets, and $\sum \cup \{ L,R\}$ is the set of actions. Does the times symbol, X, here mean the cartesian product? If so, why is the cartesian product used here?
If I undertand this correctly, $Q \times \sum$ is a function that is being mapped to $(\sum \cup \{ L,R\}) \times Q$?
Thanks!