On Tuesday, December 11, 2012 7:58:13 PM UTC-8, 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.
No, only one of the elements would need to have infinite states.
> 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?
No finite number is larger than "almost all" finite numbers.
> Personally, I don't think there is such a definition; but then I would > enjoy being proved wrong.
Within the human experience most numbers are not bound. For instance, The press will often indicate a croud is about 1.4K but not that it is about 1,440.