FEUP, The Fraction Even, Uneven Parts Hypothesis
Year: 2025
Type: article
Abstract: The Fraction Even Uneven Parts Hypothesis (FEUPH) introduces a novel and consistently valid inequality framework within rational number theory. It proposes that for any rational expression of the form mentioned in the paper there the even numerators always exceed the odd denominators under this specific structure. This holds true for all finite, and in the limit as n goes to infinity or in UCFR notation torwards +t, preserving the inequality throughout infinite repetition. Expressed in both classical and UCFR (Universal Concept of Finite Repetance) notation, FEUPH describes a symbolic sequence where the structured dominance of even-over-odd terms introduces an invariant inequality class inside the rational number set. Unlike traditional symmetric treatments of rational numbers, FEUPH uncovers a directional asymmetry based on parity, offering a new lens on number construction, sequence behavior, and structural inequality. No known prior mathematical literature, at least ro my knowledge, appears to formalize or explore this class, making FEUPH an original contribution with implications for number theory, symbolic logic, and potentially analytic function behavior. The hypothesis resists summative convergence, highlighting an important distinction from zeta-type or harmonic constructs. It remains valid across all extensions where the format is preserved, and may challenge assumptions about uniform distribution within countable rational sets. In UCFR notation it clearly shows finite results that do only divergent in the future, but are very well finite for every UCFR-logico repetance.
Author: Riedel, Bjørn Leon Søren
Institution: University of Bergen
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6912131574
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