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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
"almost
infinite" in 1615 in Joseph Hall's "No peace with Rome: wherein is
proved,
that, as terms now stand, there can be no reconcilation of the
reformed
religion with the Romish : and that the Romanists are in all the
fault"
page 101. He seems to be ridiculing the doctrine of
transubstantiation.
http://www.oed.com/search?browseType=sortDate&f_0=Full+Text&page=1&pageSize=20&q_0=almost+infinite&scope=QUOTATION&sort=date&type=dictionarysearch
http://books.google.com/books/about/No_peace_with_Rome.html?id=XCkQAAAAIAAJ
Mathematically, the term might be used in Ed Nelson's internal set
theory
to refer to a number larger than every standard number.
https://web.math.princeton.edu/~nelson/books/1.pdf
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