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