On Tuesday, December 11, 2012 10:58:13 PM UTC-5, David R Tribble wrote: > 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
A number is almost infinite if its reciprocal is almost zero. The notion of being almost zero can be given a definite sense in fuzzy logic in various ways. So - perhaps fuzzy logic can give a handle on the question.