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Re: Almost infinite
Posted:
Dec 13, 2012 8:50 AM
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I have a few small quibbles.
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.
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