Date: Dec 11, 2012 10:58 PM
Author: David R Tribble
Subject: Almost infinite
We see the phrase "almost infinite" (or "nearly infinite", or "infinite

for all practical purposes") in much literature for the layman, usually

to describe a vastly large number of combinations or possibilities from

a relatively large number of items. For example, all of the possible

brain states for a human brain (comprising about 3 billion neurons), or

all possible combinations of a million Lego blocks, etc.

Obviously, these are in actuality just large finite numbers; having an

infinite number of permutations of a set of objects would require the

set to be infinite itself, or the number of possible states of each

element would have to be infinite. Most uses of the term "infinite

possibilities" or "almost infinite" are, in fact, just large finite

numbers. All of which are, of course, less than infinity.

But is there some mathematically meaningful definition of "almost

infinite"? If we say that m is a "nearly infinite" number, where

m < omega, but with m having some property that in general makes it

larger than "almost all" finite n?

Personally, I don't think there is such a definition; but then I would

enjoy being proved wrong.

-drt