User blog:Nirvana Supermind/Generalized system for -illion-like and -yllion like suffixes

Most people reading this should know that an n-illion is 103(n+1) assuming latin prefixes. A 100 ”cent”-illion is 10^3(101) or 10^303, a 2”bi”-illion is 10^3(3) or 10^9, and so on. This -illion suffix is used in many large numbers today. A -yriad suffix represnting 102(n+1) also started being developed from an unkown source and it can be found on fakes of this wiki today.

Both of these suffixes share one thing in common: they are of the form 10x(n+1), where x is an integer assuming n is replaced with a latin prefix for n. Ηοwever this is no coincedence. This general formula applies to the suffixes -illion, -yriad, -illiob, and several more with the values of x in each affix being 3, 2, and 10^3n+3 respectively. The formula also very closely matches -plex and -noogol at x=1, but the exponents are shifted by 1.

Very recently, I had the idea to make a generalized suffix from all of these -illion-like suffixes. I called named the suffix “-illi-x-ion” and I thought it would allow for moreefficent ways of naming large numbers and for even bigger numbers to be named. This post will briefly cover this new suffix I coined and it’s uses.

First, the definition. An n-illi-x-ion, where n is swapped for the latin prefix of n, and x for a Greek prefix, is defined as the previously mentioned expression 10x(n+1), or 10xn+x. For instance, a “quadrillitriacontion” would be 10^30*4+30 = 10^150. Note that I chose a greek prefix for x because otherwise n and x might get confused due to the current numeral prefixes in googolocial use. Say in my previous example, 10^150 could be called a quadrillitrigintion which could very easily get confused with the 34-illion, which is known as a quattourtrigintillion (10^105), which is 45 orders of magnitude smaller than 10^150.

Here are some more examples:

n=30, x=1 ‘Trigintillihenion” = 10^(1*30+1) = 10^31

n=9, x=5 “Nonillipention” = 10^(5*9+5) = 10^50

n=42, x=8 “Duoquadragintillioction” = 10^(8*42+8) = 10^344

If we set the value of x in the suffix to 3, then we get the well-known -illion suffix, although using the numeral prefix system it is named “-illitrion”. Setting it to 2 creates -yriad. If you set it to 4, you result in an interesting alternative to the -illion series which is used in Chinese numerals. Since I actually was planning on proposing a system based on the -illiquadrions earlier, I might create a blog post about it soon.

Another big way such a suffix could help is by extending it to Donald Knuth’s fabricated -yllion system. An n-ylli-x-ion equates to 10^(x^(n+2)); the -yllion system in this case has a x value of 2. This would allow very big numbers to be generated as this generalized -yllion suffix quickly accelerates to double tetrational and higher growth rate once you start passing in upper Class 2/lower Class 3 numbers. For example, a googolylligoogolion is likely around 1010 10 106, which is much larger than googolplexian.

I would like to know your comment on this proposed suffix and if it is useful in googology, so comment if you have any questions.

Nirvana Supermind (talk) 07:20, July 16, 2019 (UTC)