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Re: Almost infinite
Posted:
Dec 11, 2012 11:27 PM
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On Tue, 11 Dec 2012, 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.
There are some.
Takes longer to calculate with a supercomputer than you and your kids
will live.
A hard problem taking exponential time
rather than polynomial time to calculate.
y is much greater than x, x is much smaller than y, x << y,
when for all n in Z, nx <= y.
Faster than the speed of light.
Nearly light speed, ie 180,000 miles/second or faster.
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