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2.4

2.4
The -illion Series
 CHAPTERSELECT1.1 Nature of Number1.2 Sys. of Numeration1.3 Arithmetic1.4 Properties1.5 Catalog of NumbersCosmic Horizons2.2 SI Prefixes2.3 Imagining Numbers2.4 The -illion Series3.1 Intro to Recursion3.2 Common Notations3.3 Large No. Arithmetic4.1 Jonathan Bowers4.2 Fast Growing4.3 Extensible-EAPPENDIXINDEX Continuing from our conclusion at the end of Section 2 - 3 we now want to create a naming scheme to provide some structure to the very large numbers we can generate. We will accomplish this by extending the ordinary list of -illion numbers to an utterly extreme degree. First however I will go over the history and development of the canonical -illions. Then I will discuss further possible extensions proposed by myself and many others.   Articles2.4.1 - Introduction            Before we get started, lets define what is meant here by illion series, and what requirements it must meet.   2.4.2 - Origin & Development of the -illions            I provide a brief historical tour of the origin of the -illion numbers and their development. The key subjects will be the invention of the word million, the original -illion system, and the canonical extension of it up to a vigintillion.2.4.3 - Zillions, Bazillions, Gazillions, ...            Here I discuss some of the bogus -illions and speculate as to their ranges.2.4.4 - The Great -illion Gap            I discuss the issue of the great gap of -illion names from a vigintillion to a centillion and I present a "solution" I came up with a long time ago as a kid. I also discuss how large number enthusiasts have more or less agreed to fill in the gap.2.4.5 - Prof. Henkles One million illions and Beyond!            In 1904 professor Henkle attempting to extend the illions to the millionth member. As far as I know, he was the earliest person to attempt this and get his idea published. I discuss his system and the improvements made by Mr. Ondrejka. I also suggest how the system can be extended arbitrarily.2.4.6 - Conway's & Guys Latin Based -illions            Here I discuss a logical extension of the canonical -illions proposed by John H. Conway and Richard K. Guy. Not only do they "solve" the great gap problem, but they take the Chuquet extension to it's logical conclusion !2.4.7 - Russ Rowlett's Greek Based -illions            In an attempt to resolve the conflicts of the short and long scales Russ Rowlett has proposed a greek based -illion series. In this article I extend his system to its very limit allowing us to name illions much much larger than any we can name using Conway & Guys scheme, with one small catch.2.4.8 - Jonathan Bowers 4 Tiered -illion Series            In this article we explore Jonathan Bowers' truly expansive illion Series, which goes way beyond that of Prof. Henkle or Conway & Guy. For the first time I show how the intermediate names in Bowers' system can be constructed based on Bowers' milestone examples.  2.4.9 - Donald Knuth's Naming Scheme (ON HIATUS)            Donald Knuth has proposed a novel use of the Chuquet system to allow the naming of MUCH larger powers of a thousand !   2.4.10 - Harry Foundalis' Extremely large Greek numbers (ON HIATUS)            Harry Foundalis' has discussed the greek counting system and how to extend it to absurd levels. He extends greek numbers to heights that even surpass Bowers -illion Series!