In the matter of the arrow Aristotle says that time is not composed of indivisible instants, the assumption Zeno, and that even though the arrow may not move at some point, the motion is not defined at instants but for a certain period (Katz 56-7). Aristotle was the first person who tried to deny this statement, claiming that in the example of Achilles, "a finite object can not come in contact with things quantitatively infinite," which means split-infinite time will not affect runners. Zeno paradox creates a problem for mathematicians because they are researching the idea of infinity and infinitesimals in confined spaces. He went on to say that if the time is composed of instants, the arrow never moves because at a certain instant the arrow is at a point in space but not in motion (Katz 57). Zeno said that if you start to break down a small flight time to and gradual, then you can check the arrow at a certain moment, and then the arrow will move. The second paradox studying an arrow in flight. Zeno concluded that during the tortoise has a head start, Achilles can never catch him because he will always include a limited distance in an infinite sequence of time intervals. This means that Achilles will continue to cover the distance himpunanengah gap, only to discover that he had to cover the distance himpunanengah new loopholes. However, once he closes this gap himpunanengah of the new, the tortoise would be moving again and create a new gap again. Achilles then have to close this gap himpunanengah from new before catching turtles. Then, Zeno says that Achilles himpunanelah not make himpunanengah of the original distance between himself and the tortoise, the tortoise will have moved forward, creating a new gap between the two. Zeno tells Achilles that if you want to beat the tortoise, he must first catch up with it, but to do that he first must cover himpunanengah distance between them. The first says that the tortoise and Achilles sprinter will race, and that the tortoise will be given a head start.
Two of several paradoxes that presented examples of such contradictions. Zeno, the Greek philosopher who lived in the fifth century BC, created several paradoxes to demonstrate the idea of space and time apart, and that by dividing them one comes to many contradictions. Zeno paradox with infinite, of Cantor and Russell with set theory, and the twin paradox in relativity physics has created problems and arguments for mathematicians, as well as forcing them to think about the subject of mathematics in a different way than before. An example is to say, "I always lie." If you lie, you tell the truth, but if you tell the truth, you lied. This is known as a paradox, a statement which seems to contradict themselves or appear illogical, but it still could be true. However, some seem to be no solution can be challenging and even mathematics, which is why they always cause problems such as mathematics. Mathematicians have always faced problems as they expand their knowledge of their field.