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.
Highlights
The Problem of Continuity and Discreteness is the basic problem of philosophy and mathematics
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
Analysis of the Problem of “Line Segment is Composed of Dots” by Dialectical Infinity View 1.1 Analysis of the Problem On the mathematical definition of point, it is considered that a point has no measure and a line segment has measure, but on the other hand, mathematics stipulates that ‘a line segment is composed of points’, which leads to an inherent irreconcilable contradiction in mathematics
Summary
The Problem of Continuity and Discreteness is the basic problem of philosophy and mathematics. 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.
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