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Here, I present a few silly doubts on how to define the maximum number of solutions of a polynomial using set notation and theory. Let Qn(x) be the inverse of an nth-degree polynomial. Precisely, Qn(x)=|R(x)/Pn(x)|. Here, it is of my interest to define a number, J(n), that provides the maximum number of singular points of Qn(x) or the maximum number of solutions of Pn(x)=0 since (Qn(x))-1 equals Pn(x). To that end, I have tried to create the following definition: J(n)=Sup{\gamma((Qn(x))-1=0):dQ \leq n} in which \gamma((Qn(x))-1=0) denotes the number of solutions of Pn(x)=0 and d indicates the degree of Q. Based on the above, I ask: 1. Is the above definition correct? 2. In set notation, may I use such definition "\gamma((Qn(x))-1=0)" to denote the number of solutions of Pn(x)=0? 3. Is there anything else to consider to define J(n)?