Many infinities, or only one?

In this short note we first account for Aristotle's views on infinity, by clarifying the way his notion of potential infinity should be understood, in light entelechy. We then present four distinct ways which mathematicians attempted to tame actual and ask question whether they are indeed different ways, or ultimately variations same concept. suggest that what doing is find a construct form subsumes, into itself, observe how presence former brings view about than Aristotle's.