
Re: Almost infinite
Posted:
Dec 13, 2012 2:53 PM


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

