Zeno's paradox - is it true or false?

Question

The idea is that you can never reach a destination because you would have to complete an infinate number of steps to do so. If you are not familiar with it, then please don't post an opinion. But I thought it was a very powerful evaluation on the idea of motion - that it does not exist.

Answer 1

For you to reach the destination you must get halfway there. Before you can get halfway there, you must get a quarter of the way there. Before travelling a quarter, you must travel one-eighth; before an eighth, one-sixteenth; and so on.

This infinite sequence requires you to complete infinite number of tasks in a finite time which is impossible.

But I am not too fond of Zeno and his paradoxes. Because I firmly believe that "what we are sure about in reality is not reflected in mathematics and what we're sure about in mathematics is not reflected in reality"

Answer 2

The reason why you reach your destination is that you are traversing a continuous interval with a continuous motion whose speed does not decrease to zero. This is different from a discreet motion across the same interval in which you stop and go at infinitely many points. Zeno could argue that there has to be a small dwell at each point with a lower bound, the sum of which leads to an infinite time preventing you from crossing. This is a reductio ad absurdum argument then for continuous space and continuous motion. So in conclusion i think Zeno is wrong as our everyday experience,
and Zeno's points out.

Answer 3

The rebuttal to Zeno's Paradox requires calculus. You can Google it.

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Both the paradoxes of Achilles and the tortoise and that of the dichotomy depend on dividing distances into a sequence of distances that become progressively smaller, and so are subject to the same counter-arguments.

Aristotle pointed out that as the distance decreases, the time needed to cover those distances also decreases, so that the time needed also becomes increasingly small. Such an approach to solving the paradoxes would amount to a denial that it must take an infinite amount of time to traverse an infinite sequence of distances.

Before 212 BCE, Archimedes had developed a method to derive a finite answer for the sum of infinitely many terms that get progressively smaller. Theorems have been developed in more modern calculus to achieve the same result, but with a more rigorous proof of the method. These methods allow construction of solutions stating that (under suitable conditions) if the distances are always decreasing, the time is finite....

Answer 4

this is not real; that's why that's a paradox. All you ought to do is degree out 10 ft and then walk to the ten fot mark and proceed on for therefore long as you want, thereby proving the ambiguity exciting yet faux.

Answer 5

Since they were all refuted during Zeno's lifetime, I would have to say that Zeno's paradoxes were false.

Answer 6

which one--there are several---go to:http://en.wikipedia.org/wiki/Zeno's_paradox.