Zeno's paradoxes are a set of paradoxes devised by Zeno of Elea to support Parmenides' doctrine that "all is one" and that contrary to the evidence of our senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion. Several of Zeno's eight surviving paradoxes (preserved in Aristotle's Physics and Simplicius's commentary thereon) are essentially equivalent to one another; and most of them were regarded, even in ancient times, as very easy to refute. Three of the strongest and most famous—that of Achilles and the tortoise, the Dichotomy argument, and that of an arrow in flight—are given here. Zeno's arguments are perhaps the first examples of a method of proof called reductio ad absurdum also known as proof by contradiction. They are also credited as a source of the dialectic method used by Socrates. Zeno's paradoxes were a major problem for ancient and medieval philosophers, who found most proposed solutions somewhat unsatisfactory. More modern solutions using calculus have generally satisfied mathematicians and engineers. Many philosophers still hesitate to say that all paradoxes are completely solved, while pointing out also that attempts to deal with the paradoxes have resulted in many intellectual discoveries. Variations on the paradoxes (see Thomson's lamp) continue to produce at least temporary puzzlement in elucidating what, if anything, is wrong with the argument. See http://en.wikipedia.org/wiki/Zeno's_paradoxes

There are many examples; however, most depend on the idea that motion and space are impossible... A runner is moving along a line from point A to B. The line can be spilt into an infinite amount of points, so before the ruuner reaches the end, logically, he must pass the middle of the line AB, which we will call the point C. But there are an infinite amount of points between A and C! So it can be said that he must pass the middle of the line AC, which we will call D. I'm sure you can see a pattern here! In order for the runner to reach any point on the line he must first pass the point halfway between, which in turn has another point halfway along. In other words the runner must pass an infinite number of points in order to move even the smallest distance, and by definition if we move it must take time. So here it comes... How can we pass an infinite number of points in a finite amount of time? This is the basis of many of Zeno's Paradoxes.