It’s not circular reasoning, it’s a step of mathematical induction. First you show that something is true for a set of 1, then you show that if it’s true for a set of n it is also true for a set of n+1.
Anytime you say “school” without “home” or “online” it means a building people go to. The original gets naming rights, the others have to distinguish themselves.
Well why are they paying for ads if there’s no competition