I am a young researcher and sometimes I face an uncomfortable situation : I find an error in a research paper! Of course, most of the time, it is all just my misunderstanding but it happens that after checking tens of times, there is indeed an error and therefore I am not sure what I should do. ...

My question is about closing sets under operations. First, I need a definition: Definition: Let $A$ be a set and take a function $f : A^n \rightarrow A$ for $n \in \mathbb{N}_{\geq 0}$. For a set $S$, we define the closure of $S$ under $f$, $c_f (S)$, inductively as follows: define $S_0 = S$. Fo...