An Analysis of Zeno’s Paradox and Non-measurable Sets Based on Dialectical Infinity

Abstract

The Problem of Continuity and Discreteness is the basic problem of philosophy and mathematics. For a long time, there is no clear understanding of this problem, which leads to the stagnation of the problem, because the essence of the problem is a problem of finity and infinity. The essence of the philosophical thought on which the mathematical definition of “line segment is composed of dots” is the idea of actual infinity, and geometric dot is equivalent to algebraic zero in terms of measure properties. In view of the above contradictions, this paper presents two solutions satisfying both the philosophical and mathematical circles based on the view of dialectical infinity, and the authors make a deep analysis of Zeno’s paradox and the non-measurable set based on both solutions.