Home Science Page Data Stream Momentum Directionals Root Beings The Experiment

1. The General Inverse Function0. Introduction

A. Proof: The Slope of the Difference Series for Square Roots

B. Iterative functions are weird

C. The Inverse Limit, x’

D. What does x’ equal?

E. The Inverse Fraction Series, F’

2. Dead EndsA. The Correlation & Slope Table for 3rd and 4th Roots

B. The difference between x’ and x

C. The difference between ƒ’(N) and ƒ(N)

D. Last correspondences

E. Universal Theorem for Cube Roots?

3. Organization of the Mandelbrot SetA. The Algebra of the Mandelbrot set

B. The Geometry

C. Generating Inbetween Fractions: The Process

4. The Inbetween Fractional RootA. Inbetween Theorems

B. The F Series product, neither Inbetween Root, nor Root product

C. Reexamining the Process, its Parallels

D. Inbetween Root Theorems 1 & 2

E. Other Relations, Inbetween Root Theorems 3 & 4

5. Properties of Binomial Root SystemA. Exponentiation and Multiplication

B. Implications of these properties or Vanishing Ones

C. How the F Series fits into the concept of Number

D. Cracking the iron ball to look inside

E. Primacy of ‘one’ in the exponential system

F. Parallels and Connections with the Mandelbrot Set

G. Neutralization and Transcendence

6. π and other Patterned TranscendentalsA. Micro-History

B. A Fractal Function Set for π, or another iterative series

C. π as an infinite continued fraction, a Patterned Transcendental

D. π a Ratio

E. Summary