Worth noting is that Aristotle locates the source of Zeno's paradoxes in the failure to distinguish between actuality and potentiality. Achilles does not need to actually cover an infinite number of lengths. A finite length is not actually an infinite number of lengths until we cut that length into an infinite number of lengths, which, of course, is impossible. So until you actually divide the length, the length is merely capable of being divided into an infinite number of lengths, even though it is impossible to perform that division to completion.