Section 2 - Recursion and Common Notations

2.01. Introduction to Recursion

Before we can begin looking at the popular large number notations we need to familiarize ourselves with recursion, which is arguably the single most important tool for generating large numbers. This short article explains what recursion is and why it is important to googology.

2.02. Knuth's Up-Arrows and the Hyper-Operators

Our first large number notation to examine is Donald Knuth's famous up-arrow notation, a way to generalize expressing the hyper-operators.

2.03. The Weak Hyper-Operators

The weak hyper-operators are a less powerful variant of the usual hyper-operators (the ones noted with Knuth's up-arrows). In this article we'll examine numbers that these operators make, and compare the weak hyper-operators against the normal hyper-operators.

2.04. The Ackermann Function

The Ackermann function is a famous two-argument function that has a very simple definition but produces values as big as Knuth's arrows do.

2.05. Googological prefixes and suffixes

This page talks about the Alistair Cockburn's fuga- family of prefixes and various other affixes used to name large numbers.

2.06. Joyce's googol-based naming systems

We continue from the previous page with examining a strange set of number naming systems based upon the name "googol" by a mysterious figure named Andre Joyce.

2.07. Steinhaus-Moser Notation

Steinhaus-Moser notation is another simple way to produce very large numbers, and the creators have coined some numbers with the notation: the mega, the megiston, and the Moser.

2.08. Graham's Number

Perhaps the most infamous of all large numbers is Graham's number, a number that arose from a field of mathematics called Ramsey theory. In this article I discuss not only the number commonly known as Graham's number and its history but also the other two Graham's numbers and their history, the main goal of this article being to clear up all misconceptions about Graham's number.

2.09. Conway's Chain Arrows

The most powerful of the "popular" large number noations is probably John Conway's chain arrow notation, an extension to up-arrow notation which easily makes numbers that crush Graham's number.

2.10. Extensions to Conway Chain Arrows

Some people, such as Peter Hurford, have further extended Conway chain arrows. Here we'll examine some of those extensions, and how they can be refined to be still more powerful.

2.11. Review II

I finish section 2 with a review of what we've learned in this section, and what we'll learn about in section 3.