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Achilles and the turtle
a—-“The swift-footed Achilles is in position A0 and in rectilinear distance of 100m from position X0 where a turtle is. Achilles, who is going to try to reach the turtle in a race, is running at the speed of 10m/sec, while the turtle is running at the speed of 5m/sec. The two competitors start simultaneously towards the same direction A0X0.”
b—-Zeno believes that “Achilles cannot reach the turtle if they both run in the following way: When Achilles reaches the position X0, the turtle then will have reached the position X1, having covered the distance X0X1= 50m, which will be half of the distance A0X0= 100m which Achilles ran, since the turtle will always be running at half speed of that of Achilles.”
c—-When Achilles reaches the position X1, the turtle will have reached the position X2, having covered the distance X1X2=25m.
It is clear that Achilles will never be able to reach and overtake the turtle because the latter will always preceed, even on minimum.
The walker, the arrow or Achilles and the turtle are arbitrarily chosen moving objects. In their position, any material mobile object can be placed – for example an Electron or a galaxy. Zeno chose to study the principle of movement with the use of these ordinary objects.
It is understood that neither Achilles nor the turtle are able to start (see note of paradox of the arrow.)