Fractal Analysis on the Real Interval: A Constructive Approach via Fractal Countability

Stanislav Semenov

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arXiv · 2505.13450

Fractal Analysis on the Real Interval: A Constructive Approach via Fractal Countability

Stanislav Semenov

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Abstract

This paper develops a technical and practical reinterpretation of the real interval [a,b] under the paradigm of fractal countability. Instead of assuming the continuum as a completed uncountable totality, we model [a,b] as a layered structure of constructively definable points, indexed by a hierarchy of formal systems. We reformulate classical notions from real analysis -- continuity, measure, differentiation, and integration -- in terms of stratified definability levels S_n, thereby grounding the analytic apparatus in syntactic accessibility rather than ontological postulation. The result is a framework for fractal analysis, in which mathematical operations are relativized to layers of expressibility, enabling new insights into approximation, computability, and formal verification.

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Stanislav Semenov. 2025-03-30. Fractal Analysis on the Real Interval: A Constructive Approach via Fractal Countability. https://arxiv.org/abs/2505.13450

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