
Re: Almost infinite
Posted:
Dec 16, 2012 10:33 PM


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. >
forbi...@gmail.com wrote: > No, only one of the elements would need to have infinite states.
Yes, I realized that only moments after I posted. Good to know someone is paying attention to the details.
>> 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.
Granted. Any given finite numbers is less than almost all other finite numbers.

