Let S be your set of employees and let f be your hiring function, such that f(A) = A, f(B) = C, etc. Hiring someone assessed by an employee with letter grade x

Let S be your set of employees and let f be your hiring function, such that f(A) = A, f(B) = C, etc. Hiring someone assessed by an employee with letter grade x is the union operation S U {f(x)}. There exists no map f(x) = B. The space is incomplete. Therefore, identify at least one A player and have them found a company. Then after n hires by any employee of S, S consists of n + 1 A grade employees and no other employees, because f(A) is idempotent.