I am trying to inductively prove that for any string s, the reverse of the reverse of string s is string s.
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top
The case $n = 1$ is trivial. For $n > 1$, assume that the statement holds for all $i < n$. Let $s = as'$ be a string of length $n$ where $a$ has length 1 and $s'$ has length $n - 1$. The key is to observe that rev($ab$) = rev($b$)rev($a$). Therefore rev(rev($s$)) = rev(rev($as'$)) = rev(rev($s'$)rev($a$)) = rev(rev($a$))rev(rev($s'$)) = $as'$ = $s$, thus the statement holds for strings of length $n$. We have now proved by induction that the reverse of the reverse of a string $s$ is $s$.