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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)

The problem of the relationship between the discrete and the continuous is one of the deepest and most painful in the foundations of mathematics. Classical approaches either postulate the existence of the continuum without explaining its origin, or reduce continuity to infinite c...

The Unity of the Discrete and the Continuous as a Structural Principle: The Infinium △₁ₓ₁ and the Theory of Motives

This article is devoted to one of the oldest and deepest problems in mathematics—the gap between the discrete and the continuous. We show that this gap is not an accidental difficulty but a direct consequence of choosing the structureless point as the initial primitive. Within Δ‑...