Section 3.1 - Googological Notations Part 1

This section covers large number notations up to those comparable to f_w^w(n) in the fast-growing hierarchy.

3.1.1. Introduction to the Work of Jonathan Bowers

We open up section 3 with an introduction to the work of who is arguably the most important figure in googology, Jonathan Bowers, with who he is and why is work is significant to googology. We will be focusing heavily on Jonathan Bowers' work throughout his site, so it's important for us to know who he is and the significance of his work.

3.1.2. Bowers' Linear Array Notation I

Linear array notation is the simplest subset of Jonathan Bowers' famous large number system called BEAF (Bowers' Exploding Array Function). Here we learn about the history of this notation, and examine how it works up to arrays of 4 entries, including his googolisms defined up to that point.

3.1.3. Bowers' Linear Array Notation II

In this article, we continue learning about Bowers' array notation from where we left off, from 5-entry arrays to arrays with whatever number of entries.

3.1.4. Poly-Cell Notation and Hyper-E Notation [incomplete]

Hyper-E notation is the simplest subset of Sbiis Saibian's Extensible-E system, a large number system quite similar in spirit to Bowers' large number notation which is based upon a large number notation called poly-cell notation which Sbiis Saibian came up with as a kid.

3.1.5. The Fast-Growing Hierarchy below w^w

The fast-growing hierarchy (FGH for short) is a unique large number notation that uses infinite numbers to generate large finite numbers. It is notable largely because it is the most common benchmark googologists use to compare large numbers. Here we examine a subsystem of the FGH that goes up to the ordinal w^w, which is as far as we'll go through the world of numbers in section 3.1.

[more articles planned]

3.1.X. Comparing Large Number Notations

In the last page of section 3.1, we compare all the large number notations we learned about against each other.