What does "$u(i)$" or "$v(i)$" mean in $$\{uv^R\space|\space |u|=|v| \space \text{and } \forall i \space u(i) \neq v(i)\}$$
I've seen it in my textbook, however I'm used to seeing that notation in the context of functions, so I don't get how this applies here. If anyone understands this notation I'll be thankful for a clarification.
In this context, $u(i)$ almost certainly means the letter of word $u$ at position $i$. Some authors use $u_i$ instead. Your language consists of words of the form $u v^R$ where $u$ and $v$ have equal length and differ at every position.