There first two principal ideas in relation to motion are:

• To traverse a line segment, first it is necessary to reach half of the distance. To achieve this, it is necessary to first reach a quarter of the distance and so on. Therefore an infinite number of points must be reached, which is impossible when considering this problem in a finite time.

• Consider a race between the fast running Achilles and the tortoise. It is impossible for Achilles to overtake the tortoise because when Achilles reaches the point the tortoise started at, the tortoise will have moved ahead. When Achilles reaches that point, the tortoise will have moved forward again and so on.

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