Spatial Infinities

Coordinate Systems and Geometric Space

Theorems of Spatial Infinity

How infinity manifests in coordinates and geometric constructions

Spatial infinity theorems explore the fundamental properties of infinite space through coordinate systems and geometric relationships. These proofs reveal how infinity and zero interact in spatial contexts.

Spatial Theorems (Notion)Projective Theory Core Text (PDF)

First Spatial Theorem of Infinity and Zero

Infinity and Zero of coordinates (T inf) - Infinities of Circle

The First Spatial Theorem examines how infinity appears in individual coordinate values. It explores the relationship between infinite coordinates and zero, particularly through circular geometry where points at infinity connect back to the origin.

Key Concepts

•Coordinate values approaching infinity
•Circular geometry and infinite points
•The relationship between infinity and zero in coordinates
•T infinity as a coordinate transformation

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Second Spatial Theorem of Infinity and Zero

Infinity and Zero of coordinate systems (R inf)

The Second Spatial Theorem extends the analysis to entire coordinate systems rather than individual coordinates. It examines how coordinate systems themselves can be infinite or approach zero, revealing deeper structural properties of space.

Key Concepts

•Coordinate system transformations at infinity
•R infinity as a system-level property
•Relationships between different coordinate systems
•Structural infinity in geometric spaces

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