TED-Ed: What is Zeno's Dichotomy Paradox? - Colm Kelleher

The video explores Zeno of Elea's paradoxes, focusing on the dichotomy paradox, which suggests that motion is impossible because one must traverse an infinite number of finite steps. The paradox is resolved mathematically by showing that an infinite series of finite terms can sum to a finite value. This is illustrated using a geometric approach, where a square is divided infinitely, yet the total area remains finite, demonstrating that Zeno's journey to the park takes a finite time.

Who was Zeno of Elea and what is he best known for?

• A Roman philosopher known for his work on ethics

• A Greek philosopher famous for his paradoxes

• An Egyptian mathematician known for geometry

• A Persian scientist known for astronomy

What is the main idea behind Zeno's dichotomy paradox?

• That time is an illusion

• That space is infinite

• That numbers are finite

• That motion is impossible

According to Zeno's paradox, what happens to the distance Zeno needs to travel?

• It disappears completely

• It is divided into infinitely smaller parts

• It remains constant

• It becomes larger with each step

How is the paradox resolved mathematically?

• By proving that infinity does not exist

• By demonstrating that time is not real

• By showing that an infinite series can sum to a finite number

• By concluding that motion is indeed impossible

What example is used to illustrate the resolution of Zeno's paradox?

• A line being divided into segments

• A square being divided into smaller areas

• A triangle being divided into smaller triangles

• A circle being divided into arcs