Setup: Achilles and the Tortoise engage in a race, but the tortoise is given a head start, while Achilles is the faster racer.
Premise 3 is false because looking at all the points when Achilles reaches a midpoint is only looking at a sequence of points that get closer together, and thus correspond to points in time that get closer together (by proportionality through velocity). Since they are midpoints, it is a standard convergent geometric series. By thinking about the situation, you can realize that the points in time converge to the point where Achilles passes the Tortoise. Clearly if we only look at points in time before the passing ocurrs, we will never observe the passing itself, but this does not imply that the passing never occurs in the real world.