  The tortoise will again have progressed some further distance  (d3) beyond t2, namely to  t3, in the time it takes Achilles to move from  a2(=t1) to  a3(=t2). In fact, during the  time it takes Achilles to reach the tortoise’s location at the  beginning of that time, the tortoise will always have moved some  distance ahead, so that every time Achilles reaches the tortoise’s  new starting point, the tortoise will be ahead some. Therefore, the  slowest runner in the race, the tortoise, will never be overtaken by  the fastest runner, Achilles.