The term "googolism" is used loosely on this wiki, but what qualifies exactly as a googolism?
Is Graham's Number a googolism? What about eight-nonillion-nine-hundred-ninety-octillion-eight-hundred-seventy-four-septillion-three-hundred-eighty-nine-sextillion-seventy-nine-quintillion-eighty-seven-quadrillion-four-hundred-ninety-trillion-eight-hundred-fifty-seven-billion-nine-hundred-four-million-eight-hundred-twenty-nine-thousand-forty-seven? How about pi or e ? one,two,three? zero, negative one? one half? googolminex? googolminex and one ? the imaginary unit ? Box_M~ ? Sam's Number ? Promaxima ? TREE(3) ?
Is a googolism simply a number? If so then why does the wiki say named numbers are prefered? Aren't all integers named by their decimal expansions? If a googolism is a named number ... then aren't a giggol and a hectalogue the same googolism. What about googolquinplex and googolquintiplex?
Here is my answer: A googolism is a number name. In other words it's a specific name assigned to specific number. In it's most general sense then, even pi and e are googolism's because they are specific names created to provide a name for these specific irrational constants. When Graham's Number was defined, this was not a googolism, but when Gardner dubbed this number Graham's Number he was coining a googolism.
What makes a googolism distinct? Since a googolism is simply a number+name two googolism's are the same if and only if both the name and the number they represent are the same. So giggol and hectalogue are distinct googolism's. So are great googol = E1000 and great googol = E100##1#2. googolquinplex and googolquintiplex is debatable. I'd say we might include variations of spelling as the same googolism, but the alternate spellings may also be considered distinct. Certainly googolduplex and googolplexian are distinct.
There are some extreme cases to consider. Promaxima, Sam's Number, and TREE(3), as well as stuff like one half, the square root of two, and the imaginary unit. In the cases of one half, square root of two, and the imaginary unit, although these are specific names for specific numbers, we may restrict the domain of googolism's to only include positive integers. What about Skewes' number then? We might extend this then to non-negative reals. For numbers which don't have any names except mathematical expressions, we may not consider this a true googolism. A googolism is usually understood as a word which is a stand-in for a number or mathematical expression. The wiki, for example, does not consider TREE(3) a googolism as it is not an official entry. Is Tree-Three a googolism? Then there are numbers which are either difficult to define precisely or at all like promaxima or Sam's Number? Are these googolisms? I think we can agree that things like many, a lot, few, several, a zillion, etc. are not googolism's. These are vague quantifiers. They aren't intended to represent a specific quantity, only the vague idea of a quantity. So what about vaguely defined numbers? If the intention is to define a specific value it's a googolism.
This definition may appear too generous to some, and impractical for classification purposes here at Googology Wiki. What do you think? What defines a googolism? Is this wiki about collecting and organizing googolisms? If so what makes googolism's distinct?
I'm interested to hear what other people have to say on the subject.