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2-4-2 : Zillions, Bazillions, Gazillions, ...

Zillions, Bazillions, Gazillions, ...

What is a Zillion ?

How many zeroes does a zillion have? Kid's often ask this. In fact when I was a kid I was asked this by some other kids who figured I would know since I was such a "math whiz". I told them that there was no such number, but if there was it would be written out like this... and I preceded to write a 1 followed by groups of 3 digits on and on without stopping...

1,000,000,000,000,000,000,000,...

...which astounded my audience with an audible gasp. I continued until the teacher finally decided I was a distraction and told me to stop. I probably gave those kids the impression that a zillion really was a number, but what I had said initially was true. "Zillion" is not any specifically defined number. It's earliest known use was in 1934 [1] . Most likely in response to the "absurd" proliferation of -illion names all the way up to vigintillion, people started to use the term "zillion" simply as a joke meaning some really unfathomably large number. Logically we can at least assume that a "Zillion" is some vastly large power of 1000, but which? Certainly it could not represent any commonly known -illion, since it is meant to sound esoteric. So a zillion is certainly larger than a million, a billion, a trillion, etc. Just how far out does it go then? That's where it becomes arbitrary. Zillion may represent ANY very large power of a thousand, certainly larger than a trillion, and maybe even a vigintillion or centillion !

Just as a million had spawned the Chuquet illions, the "zillion" also had many follow ups. The first use of the term "Jillion" was in 1942 [2] , and the first use of "gazillion" was in 1977 [3] . Since then there has been an explosion in number of terms, with too many to mention.

Some of the most common ones are: zillion, gazillion, jillion, gajillion, bazillion, bajillion, etc.

There seems to be some agreement that some of these are unfathomably larger than some others, though of coarse, not by any specified amount.

One source actually provides this convenient ranking system. We can say that zillion and jillion are roughly in the same class in terms of vastness. Beyond these lie the more ginormous bazillion and bajillion. Beyond even these are the incomprehensible gazillion and gajillion [4] .

As a kid I wasn't actually that fond of a term like "zillion". I liked numbers to mean something. This is the essense of why I tried to write out a zillion. It wasn't because I mistakenly believed it was a number; it was because I thought it should be given an exact value. Of coarse anyone can go ahead and define a zillion to be an exact value, that after all is the essense of large numbers (the implicit right you have to name the numbers you can reach anything you like). There are two problems with this however. First and foremost, anything you would choose would be seemingly arbitrary, and probably seem too small as well ( there's nothing larger than a free-floating imagination). Secondly people would still want to have a meaningless word to describe an indescribably large number, so some other term would have to be invented to take the place of a zillion, thus defeating the original purpose. None the less, many have tried to pin down exact values for these numbers.

For example:

A guy named greg actually provides a definition for a gazillion. He claims that "gaz" is actually latin for earthly edge. Assuming this to mean the earths circumference in greek miles, which he claims to be 28,810, he defines a gazillion as 1 followed by 28,810 sets of zeroes. Thus...

A gazillion = 10^86,430

He even bothers to write this out in full [5] !

Personally I don't think this is large enough. I'd say even a zillion is "alittle" larger than this. I'd say a gazillion must have at least a zillion zeroes or around about!

I myself have attempted to provide a definition for a zillion, but none has really stuck. Of coarse we want some kind of rational for a definition, but a zillion offers none. The best I think we can offer is that these numbers should be bounded by certain ranges. Certainly a "zillion" means a very large number, but for those who actually know anything about large numbers, there is always a more infathomable infathomable further down the road. Can we put an upper bound on how large a zillion is?

One would have to consider the context in which zillion is usually used and decide based on this. Most people seem to mean a ridiculously big number well beyond a trillion. I think it's safe to say most people are refering to some astronomical sized number, probably somewhere between a vigintillion and a centillion. Another more radical use might be to describe a number with so many zeroes that a person could never write it out. In that case a zillion would need at least a billion zeroes or so.

Consider this: which do you percieve as bigger. A zillion or a googolplex? If you here a googolplex as larger than we could say that provides an upperbound. If not then a zillion has to be at least larger than a googolplex. I think placing a zillion in that fuzzy space between centillion and a googolplex is a good place to start. A Bazillion can then have at least a zillion zeroes, and a Gazillion at least a bazillion zeroes.

Or perhaps it's best to simply think of a zillion as a generic member of the -illion series, preferably a largish one. Maybe a Bazillion transcends all the currently named -illions and a Gazillion transcends any that could reasonably be named.

Having a label for a "range" is actually somewhat useful for the subject of large numbers, and a zillion, bazillion, and gazillion, are certainly suited to this end. However they really originate as humor or indefinitely large. It was never meant to be taken seriously.

Conclusion

As long as we know that "zillion" isn't officially recognized, and that it means "indefinitely large" we can speak about it. We can define a number and name it a "zillion", but the concept of a zillion will remain. In my book I see no problem with people defining and naming any large numbers they like, as long as they make it clear that it is their own coinage. It would be misinformation for someone to claim that their definition for a zillion was the "true" definition. That's what hoaxes are all about. But as I see it someone can define their own "zillion" as long as they provide some kind of disclaimer.

In any case, we don't have much use for in exact number here. It is certainly possible to come up with many well defined -illion numbers outside the canonical 21 names mentioned in the first article.

In the next article I discuss how I tried to fill in the gap between a vigintillion and a centillion as a kid.