Section 1: Basic Numbers, -illions, and Astronomical Magnitudes
"The interesting thing though is, the googolplex is not a chimera, it actually exists! The googolplex's days are numbered."
—Sbiis Saibian (source)
1.01. Numbers in the English language
We'll open up this site with a discussion of numbers in the English language, with their usage, naming, and origins. Then, we'll go through the basic operators in mathematics, as a warm-up for the powerful googological functions we'll see later.
Next, we'll go into more detail into the -illions, and discuss how they are used today using a Google search.
1.03. Sizes of the -illions: Magnitudes in the Physical World
Now let's go into high gear and take an extensive tour of the -illions and how big they really are, with magnitudes in the physical world. For example, how much space would a quintillion gallons of water take up, and would a vigintillion atoms be enough to fill up the earth?
Next, I discuss the pair of legendary large numbers, the googol and the googolplex, along with popular extensions to them like the googolduplex, -triplex, and so on.
1.05. Large Numbers in Probability
Probability and combinatorics allow us to generate much larger numbers than the physical world does. This article is a tour of the wide variety of numbers that arise from probability in increasing order of size.
Another famous pair of numbers in the range we'll cover here is the two Skewes' numbers, which are large upper bounds to a problem involving the distribution of prime numbers. Here I'll explain the problem they came from, and then try to get a sense of their size as well as their further history.
1.07. Extending the -illions I: Henkle, Conway, and Rowlett
This page discusses some of the systems people have used to extend the -illions way beyond the googol and googolplex.
1.08. Extending the -illions II: Jonathan Bowers' -illions
In this article we continue extensions to the -illions by examining an extensive naming scheme by Jonathan Bowers.
1.09. Extending the -illions III: Knuth's -yllions and Further Extensible Systems
Here we'll examine a complete revamp of the entire idea of -illions known as the -yllions devised by Donald Knuth. Furthermore we'll examine an extension that goes way further than previous systems and lacks many of the other systems' drawbacks, and how to apply that to the usual -illions.
Let's review what we've learned in this section, and preview how we can really crush all those smaller numbers.