How did Zeno of Elea use reductio ad absurdum arguments?

Zeno of Elea utilized reductio ad absurdum to defend the monistic philosophy of his teacher, Parmenides, who argued that reality is a single, motionless entity.123

Rather than arguing for his own position directly, Zeno employed a method of dialectic that began with his opponents' premises—specifically the common-sense beliefs that a plurality of things exists and that motion is real. He then demonstrated that these assumptions inevitably lead to logical contradictions or absurd conclusions.2314

For example, in his arguments against plurality, Zeno showed that if reality were composed of many distinct things, those things would have to be both finite and infinite, which is a contradiction. Similarly, in his famous paradoxes of motion, such as the Achilles and the tortoise, he argued that the assumption of motion requires traversing an infinite number of points in a finite time. By showing that these premises result in logical impossibilities, Zeno sought to discredit the belief in plurality and motion, thereby reinforcing the Parmenidean doctrine that reality is one and unchanging.132