What question did this study set out to answer?

To resolve the classical mathematical paradox between discrete and continuous domains by proposing a geometric structural primitive rather than a structureless point.

August 20, 2026Open Access

The Infinium as a Bridge Between the Discrete and the Continuous: The RIT and Its Motive Structure (Why a Single Triangle Resolves the Oldest Paradox of Mathematics)

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To resolve the classical mathematical paradox between discrete and continuous domains by proposing a geometric structural primitive rather than a structureless point.
Formulated a framework within delta-ontology using the right isosceles triangle with legs of 1 and hypotenuse of square root of 2 as the fundamental quantum.
Derived the motive structure formalization combining orthogonality, self-similarity, and irrational measures across number systems.
Demonstrated that the triangle motive structure unites discrete counting and continuous geometry without postulating arbitrary infinite constructions.
Showed that the choice of this geometric primitive provides a unified structural framework capable of contextualizing major mathematical conjectures and number systems.

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Implication

Theoretical analysis demonstrates that using a right isosceles triangle primitive unifies discrete and continuous systems, suggesting a foundational resolution to classic mathematical paradoxes.

Cite This Study

Petrov et al. (2026) studied this question.

synapsesocial.com/papers/6a86b56c8a91293e6a1ccbea https://doi.org/10.5281/zenodo.21996007

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Implication

Theoretical analysis demonstrates that using a right isosceles triangle primitive unifies discrete and continuous systems, suggesting a foundational resolution to classic mathematical paradoxes.

The Infinium as a Bridge Between the Discrete and the Continuous: The RIT and Its Motive Structure (Why a Single Triangle Resolves the Oldest Paradox of Mathematics)

Key Points

Discussion

Implication

Cite This Study

The Infinium as a Bridge Between the Discrete and the Continuous: The RIT and Its Motive Structure (Why a Single Triangle Resolves the Oldest Paradox of Mathematics)

Key Points

Discussion

Implication

Cite This Study

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