Dualistic Wave: A Proposed Explanation of Zenos Paradox

In this paper, a novel geometric object named dualistic wave is established and employed to solve the dilemma of Zeno’s paradox. In one period, a dualistic wave is composed of four curved infinitesimal line segments and each of them is equivalent to a flat infinitesimal line segment. A dualistic wave can be viewed as an infinitely small wavelike space or an infinitely small flat space; they are equivalent. Intuitively, the ingredient of a straight line is obviously an infinitesimal straight line segment. However, it is shown that the ingredient can also be viewed as an infinitesimal curved line segment. An infinitesimal line segment is classified into two categories: flat infinitesimal line segment and curved infinitesimal line segment. The equivalence between a flat infinitesimal line segment and a curved infinitesimal line segment is demonstrated. This is based on the concept of equivalent infinitesimal in calculus. The mathematical equations describing dualistic waves constructed by different curved infinitesimal line segments are given.