• Firstly, we assume that a line segment is made up of a multiplicity of points. From this assumption a line segment can always be bisected. Every bisection results in a further line segment that can itself be bisected. The bisection process can be repeated continuously without there ever being a stopping point. Therefore a line segment cannot be made up of points.

• That the continuous, the line, must be both finite and infinite in the number of points it contains. It must be finite because it contains as many points as it contains, no more or less. On the other hand, the continuous must also contain an infinite number of points, for it is infinitely divisible. Hence there is a contradiction to the assumption that a line is composed of a multiplicity of points.

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