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Topic: Almost infinite
Replies: 19   Last Post: Mar 21, 2013 2:40 PM

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Posts: 1,327
Registered: 11/29/07
Re: Almost infinite
Posted: Dec 13, 2012 2:53 PM
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On Dec 11, 7:58 pm, David R Tribble <da...@tribble.com> 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.
> -drt

Oxford English Dictionary has the first occurrence of the phrase
infinite" in 1615 in Joseph Hall's "No peace with Rome: wherein is
that, as terms now stand, there can be no reconcilation of the
religion with the Romish : and that the Romanists are in all the
page 101. He seems to be ridiculing the doctrine of



Mathematically, the term might be used in Ed Nelson's internal set
to refer to a number larger than every standard number.

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