What is word reversal $w^R$? In the following context, what is the _formal_ meaning of "reversal of word $w$"? > The free monoid on $A$ is the syntactic monoid of the language $\\{ ww^R\ |\ w \in A^*\\}$, where $w^R$ denotes the reversal of word $w$.

Formally, elements of $A^*$ are _finite sequences_ of $A$, that is, _functions_ $\\{1,2,\dots,n\\}\to A$ for some $n\in\Bbb N$. Then, if $w=(a_1,\dots,a_{n})$ then we define $$w^R:= (a_n,\dots,a_1):=i\mapsto a_{n+1-i}$$