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4.1


4.1

The Astounding Work of Jonathan Bowers

CHAPTER
SELECT
1.1 Nature of Number

1.2 Sys. of Numeration
1.3 Arithmetic
1.4 Properties
1.5 Catalog of Numbers
2.1 Cosmic Horizons
2.2 SI Prefixes
2.3 Imagining Numbers
2.4 The -illion Series
3.1 Intro to Recursion

3.2 Common Notations

3.3 Large No. Arithmetic

4.1 Jonathan Bowers

4.2 Fast Growing

4.3 Extensible-E



   We begin our development of a general theory of recursion by exploring the work of the father of modern googology: Jonathan Bowers. His work goes well beyond that of other amateurs and is on par with the "fast-growing hierarchy" of professional mathematics! His work has inspired many a would-be googologist, and his work has been the inspiration for even deeper studies into large numbers and recursive functions. I would go so far as to say Jonathan Bowers' put googology on the map! For this reason we will begin our study of general recursion with Jonathan Bowers' infamous Exploding Array Function (referred to whimsically as BEAF by Bowers himself)

4.1.1 - The Infamous Jonathan Bowers : Who is Jonathan Bowers, and why is his work significant for the rest of our discussion throughout section IV? Read and find out.

4.1.2 - Bowers' Extended Operator Notation : We now begin to reconstruct the early work of Jonathan Bowers. Here we explore his original 2002 Extended Operator Notation.

4.1.3 - Bowers' Array Notation (ON HIATUS)

4.1.4 - Bowers' Extended Array Notation (ON HIATUS)

4.1.5 - Bowers' Super Extended, Exploding, & Super Extended Exploding Arrays (ON HIATUS)