I am totaly new to theoretical computer science, so I am sorry if I get the terminology wrong:
I was reading the definition of a grammar, what I didn't get was the formal definition of the production rules: Let V be the set of Variables and sigma the alphabet. Let P be the set of Rules or productions. Formal: $P \subset (V \cup\sum)^+\times (V \cup\sum)^*$.
I saw an example with G = ({P}, {0,1}, A, P) with the set of rules A:
1.P $\to \epsilon$
2.P $\to 0$
2.P $\to 1$
4.2.P $\to 0P0$
Now my question: How can the last rule (no 4) exist? It is not an element of the subset of the cartesian product mentioned above.