 One aspect of the paradox is thus that Achilles must traverse the following infinite series of distances before he catches the tortoise: first 0.9m, then an additional 0.09m, then 0.009m, …. These are the series of distances ahead that the tortoise reaches at the start of each of Achilles’ catch-ups. Looked at this way the puzzle is identical to the Dichotomy, for it is just to say that ‘that which is in locomotion must arrive [nine tenths of the way] before it arrives at the goal’. And so everything we said above applies here too.