My Ultimate Unified Formula of the Universe: The Infinite Halving Principle and Convergence to One - Visual Proof by Ruel Villaber

Abstract:

This work presents a visual and mathematical demonstration of the Infinite Halving Principle as conceptualized by the author. The core concept shows that unity (1) can be exactly formed through infinite halving.

Summary Concept:

1 = 1/2 + 1/2

and

Sum_{n=1}^{∞} (1/2)^n = 0.5 + 0.25 + 0.125 + ... = 1.0 EXACT

Detailed Core Formula:

CONVERGENCE TO ONE:

S_n = 1/2 + 1/4 + 1/8 + 1/16 + ... + (1/2)^n

Formula: Sum_{n=1}^{∞} (1/2)^n = 1

Sum formula: S_n = 1 - (1/2)^n

Limit: lim_{n→∞} S_n = 1

The Infinite Halving Principle:

1/2 + 1/4 + 1/8 + ... = 1

1 - 1/2 - 1/4 - 1/8 - ... = 0

This preprint includes photographic evidence of the author holding the original formula poster as proof of authorship and original presentation.

Author: Ruel Villaber

Independent Researcher, Mandaluyong City, Philippines 2026

Type: Preprint, Visual Mathematics, Educational Material

License: CC BY 4.0