Abstract

Certain areas in mathematics seem to possess deep secrets. Such are the areas of mathematics that deal with the concepts of infinity. The concepts of infinity have always stirred great emotions and produced seemingly unsolvable paradoxes. One such paradox is Zeno's paradox of Achilles. We begin our research by examining the times in which Zeno lived, the intellectual arguments of that time, and the reasons why Zeno formulated his paradoxes. We will also examine what effects this paradox had on the development of mathematics. This analysis will include Aristotle's formulation of the paradox and the general problems of actual infinity. The two views on the structure of matter and how the paradox is dealt with according to each view will also be covered. Next, we will examine various ways the paradox could be explained: From a mathematical point of view we will examine the paradox in terms of limits, transfinite numbers and through geometric proofs. Then we will examine some of the philosophical explanations, and how the two views on the structure of matter explain the paradox. Finally we will examine how the concept of infinity is dealt with in Jewish philosophy and what bearing this may have on the explanation of the paradox. We will conclude by listening to two pairs of students' spontaneous explanation of the paradox and examining if students background may have any affect on the way they explain and understand the paradox