User blog:B1mb0w/The (new) J Function

The J Function
The J function is a reasonably fast growing function that will be progressively modified to simplify its presentation and increase its rate of growth. This blog will explain the structure of the function and will give various calculated values. The J Function will then be used by a brand new version of the Alpha function. Click here for more information about the Alpha Function.

Definition
The J Function uses algorithms defined in sandpit blogs. The sandpits help to illustrate how the J Function has evolved and where it is leading to.

The sandpits can be split into two types of functions (1) Notational and (2) Computable. The key difference is that:

(1) Notational functions generate text strings of actual FGH functions using various Veblen Hierarchy ordinals.

(2) Computable functions are based on mathematical functions that calculate explicit (large) finite numbers for various input parameters.

Comparison of the J Function Sandpits
The following is a summary of the results from the J Function sandpits to date.

Other approaches will be used to exceed epsilon_0 and explore the Veblen hierarchy. Refer to my other Sandpit \(J_4\) blog. This section will be re-written to use that approach instead.

WORK IN PROGRESS

Comments and Questions
Look forward to any comments and questions. If anybody is interested, the J Function was named by my wife. The full name is the Juki Function.

Cheers B1mb0w.