1 votes 1 votes Use induction on $n$ to show that $|u^n|=n|u|$ for all strings $u$ and all $n$. Theory of Computation peter-linz peter-linz-edition4 theory-of-computation proof + – Naveen Kumar 3 asked Mar 17, 2019 Naveen Kumar 3 283 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes Solution from Peter Linz itself: For $n = 1,$ $|u^1| = |u|.$ Assume $|u^k| = k|u|$ holds for $k = 1, 2, ..., n,$ then $|u^{n+1}| = |u^nu| = |u^n| + |u| = n|u| + |u| = (n + 1)|u|.$ Detailed Video Solution Deepak Poonia answered Aug 11, 2022 Deepak Poonia comment Share Follow See all 0 reply Please log in or register to add a comment.