Mathematical Demonstration of the Continuity of Time and Space presents a rigorous, self-contained analysis showing that a limit point added at infinity can be reached with full continuity, differentiability, and infinite smoothness. Using a simple refinement sequence and a standard change of variables, the work proves that the limiting value is not a singular boundary: the function is continuous at infinity, its derivative at infinity exists and equals zero, and all higher-order derivatives vanish as well. Beyond the formal result, the paper clarifies a common conceptual error in physics: finite measurement resolution does not imply ontological discreteness. “Minimum measurable” intervals reflect experimental limitation, not a breakdown of continuity. The article is written to be readable, rigorous, and directly relevant to debates on spacetime granularity, limits, and the logic of inference from finite observations.
Date: Dec 26, 2025
Author: Carlos Omeñaca Prado
ORCID: https://orcid.org/0009-0001-9750-5827
Resource type: Preprint
Publisher: Zenodo
License: CC BY-SA 4.0 International
Related links:
- https://zenodo.org/records/18093432
- https://archive.org/details/mathematical-demonstration-of-the-continuity-of-time-and-space-limits-smoothne
- https://www.academia.edu/145694149/Mathematical_Demonstration_of_the_Continuity_of_Time_and_Space_Limits_Smoothness_and_Finite_Resolution