We show that all known types of spaces and manifolds — from Euclidean and Hilbert spaces to Kähler, spin, and supermanifolds — are not independent constructions but are generated from a single fundamental object: the infinium ℑ = △₁ₓ₁ (a right isosceles triangle with legs 1 and hypotenuse √2). The key fact is that all these spaces are defined via Cartesian coordinates, and Cartesian coordinates are nothing other than a system of orthogonal legs of the infinium. Since the infinium possesses the properties of orthogonality, self-similarity, irrationality of √2, and an intrinsic measure, all spaces formulated in Cartesian coordinates automatically turn out to be its projections, deformations, or derivatives. We provide explicit generation formulas for each type of space, present a categorical scheme, and a logical closure through forcing (⊩). This approach resolves the fundamental contradiction between the discrete and the continuous, and also explains why mathematics built on Cartesian coordinates describes physical reality so effectively.
Alexey (KAMAZ) Petrov (Thu,) studied this question.