Essential Infinities

Three categories of mathematical proofs exploring the fundamental nature and behavior of infinite systems

Foundation: Five Theorems and Three Methods
The theoretical framework underlying all infinity proofs

The Laegna approach to infinity is built on five fundamental theorems organized into three methodological categories. Each category represents a distinct way of understanding and working with infinite systems.

Three Categories of Infinity Proofs

Spatial Infinities
Theorems about coordinates, coordinate systems, and geometric space

Spatial infinity theorems explore how infinity manifests in coordinate systems and geometric constructions. These proofs reveal fundamental properties of space at infinite scales.

First Spatial Theorem

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

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Second Spatial Theorem

Infinity and Zero of coordinate systems (R inf)

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Infinity Mapping
Function-based approaches to discrete numbers and infinite limits

Infinity mapping theorems establish relationships between infinite and finite domains through functional transformations, revealing how infinity can be mapped to discrete structures.

Infinities and Discrete Numbers

Mapping infinite systems to discrete numerical structures

Limits of Infinite Functions

Finite functions of infinity mapping and their limiting behavior

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Infinite Geometry
Projective geometry theorems and geometric relations at infinity

Infinite geometry theorems apply projective geometry principles to understand how geometric relationships behave at infinite scales, including angular relationships and differentiation.

90 Degree Angles

Orthogonal relationships in projective infinite geometry

Differentiation and Acceleration

Calculus concepts extended to infinite geometric systems

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