# What was Zeno trying to prove?

## What was Zeno trying to prove?

This first argument, given in Zeno’s words according to Simplicius, attempts to show that there could not be more than one thing, on pain of contradiction: if there are many things, then they are both ‘limited’ and ‘unlimited’, a contradiction.

In its simplest form, Zeno’s Paradox says that two objects can never touch. The idea is that if one object (say a ball) is stationary and the other is set in motion approaching it that the moving ball must pass the halfway point before reaching the stationary ball.

What is Zeno best known for?

Zeno’s paradoxes have puzzled, challenged, influenced, inspired, infuriated, and amused philosophers, mathematicians, and physicists for over two millennia. The most famous are the arguments against motion described by Aristotle in his Physics, Book VI.

### What is the point of Zeno’s paradox?

Thus Plato has Zeno say the purpose of the paradoxes “is to show that their hypothesis that existences are many, if properly followed up, leads to still more absurd results than the hypothesis that they are one.” Plato has Socrates claim that Zeno and Parmenides were essentially arguing exactly the same point.

No matter how small a distance is still left, she must travel half of it, and then half of what’s still remaining, and so on, ad infinitum. With an infinite number of steps required to get there, clearly she can never complete the journey. And hence, Zeno states, motion is impossible: Zeno’s paradox.

So in short, Zeno’s paradoxes were not paradoxes but were just errors in his thinking. It was not evident at the time since humans had more vague notions of concepts like number, measurement, infinity, time, motion etc. Calculus is not resolving this so-called paradox, it does something entirely different.

Or, more precisely, the answer is “infinity.” If Achilles had to cover these sorts of distances over the course of the race—in other words, if the tortoise were making progressively larger gaps rather than smaller ones—Achilles would never catch the tortoise.

Is there a solution to Zeno’s paradox?

Although the numbers go on forever, the series converges, and the solution is 1. As long as Achilles is making the gaps smaller at a sufficiently fast rate, so that their distances look more or less like this equation, he will complete the series in a measurable amount of time and catch the tortoise.

From Simple English Wikipedia, the free encyclopedia Zeno’s paradoxes are a famous set of thought-provoking stories or puzzles created by Zeno of Elea in the mid-5th century BC. Philosophers, physicists, and mathematicians have argued for 25 centuries over how to answer the questions raised by Zeno’s paradoxes.

### Did Cantor solve Zeno’s Paradox?

These accomplishments by Cantor are why he (along with Dedekind and Weierstrass) is said by Russell to have “solved Zeno’s Paradoxes.” That solution recommends using very different concepts and theories than those used by Zeno.

What is Zeno’s argument?

By a similar argument, Zeno can establish that nothing else moves. The source for Zeno’s argument is Aristotle ( Physics, Book VI, chapter 5, 239b5-32). The Standard Solution to the Arrow Paradox requires the reasoning to use our contemporary theory of speed from calculus.

Does Zermelo-Fraenkel set theory solve the Zeno’s Paradox?

That controversy still exists, but the majority view is that axiomatic Zermelo-Fraenkel set theory with the axiom of choice blocks all the paradoxes, legitimizes Cantor’s theory of transfinite sets, and provides the proper foundation for real analysis and other areas of mathematics, and indirectly resolves Zeno’s paradoxes.