I am trying to understand the following definition of prefix set - "A prefix set is a language $A \subseteq \Sigma^*$" such that no element of A is a prefix of any other element of A.
I came across a similar phrase in Li-Vitányi's book, "no element in the set is a proper prefix of another element in the set".
Can someone please elaborate on this? Perhaps an example will help me understand it. I couldn't find the explanation for this on Wikipedia or on Math.SE
A word $p$ is a prefix of a word $u$ if there exists a word $s$ (possibly the empty word) such that $u = ps$. Let $A$ be an alphabet. A subset $P$ of $A^*$ is prefix if the conditions $u, v \in P$ and $u$ prefix of $v$ imply $u = v$. For instance, $\{aa, ab, b\}$ is prefix, but $\{aa, ba, b\}$ is not since $b$ is a prefix of $ba$.