Zeno's paradox and its contributions to the notion of infinityName: Dejvi DashiSchool: King's-Edgehill SchoolIB nr: 000147-0006Mathematical explorationMay 2014Date: March 31, 2014Word count: 2681Achilles and the tortoise is one of the many mathematical and philosophical paradoxes expressed by Zeno of Elea. His goal was to present the idea that movement is just an illusion. Many solutions have been proposed for many years to explain these paradoxes. Some of these solutions include the time factor, arguing that a mathematical result can be obtained when a certain time is set for the race. However, many others have concluded that solutions, which include a fixed deadline, have simply missed the gist of Zeno's paradoxes. There is also a philosophical process that many mathematicians have had to undertake in order to expand the network of solutions to these problems. Mathematicians like Weierstrass and Cauchy propose methods that are achieved through a fusion of mathematical ability and reasoning. Zeno's paradoxes have led to many contributions in mathematics and calculus through attempts to understand them. My goal is therefore to analyze how the mathematical solutions contributed to a better understanding of the philosophy behind Zeno's problems.1. Achilles and the TurtleAchilles is about running a race against the turtle and the turtle has a head start due to the idea that he is weaker. Zeno claims that Achilles will never be able to reach the turtle, no matter how fast he runs. In order for Achilles to reach the turtle, he must first travel the distance he was initially given. In doing so, the turtle will...... middle of paper ......trass saw these problems from a purely mathematical point of view and this helped them redefine the mathematical concept of limit. Others have thought of these paradoxes as a way of fueling our skepticism and doubting the deficiency of what we assume. It seems to me that we can benefit from these problems now too. Looking at the proposed solutions over the years, I think the search for a "proper" solution shows an interest in whether Zeno's ideas can be foiled rather than knowing what his goal actually was. A paradox is meant to juggle the value of truth in a statement and I think Zeno was well aware of this when he came up with them. Therefore, although they had massive impacts in many fields, Zeno's paradoxes were an invitation to open skepticism towards our presumptions and, therefore, to a sharper but broader perception of mathematics..