\begin{frame}{Operations on Words} \begin{block}{Concatenation} If $v = a_1 \cdots a_n$ and $w = b_1 \cdots b_m$, then \begin{talign} \alert{vw} = a_1 \cdots a_n b_1 \cdots b_m \end{talign} \end{block} \begin{exampleblock}{} The concatenation of $abb$ and $ba$ is $abbba$. \end{exampleblock} \pause\bigskip \begin{block}{Length} If $v = a_1 \cdots a_n$, then $\alert{|v|} = n$. \medskip The length can be defined inductively: \begin{talign} |\lambda| &= 0 & |va| &= |v|+1 \end{talign} \end{block} \begin{exampleblock}{} The length of $abbba$ is $|abbba| = 5$. \end{exampleblock} \end{frame}