Path: utzoo!utgpu!news-server.csri.toronto.edu!rpi!zaphod.mps.ohio-state.edu!wuarchive!rex!uflorida!gatech!purdue!haven!ncifcrf!lhc!adm!smoke!gwyn
From: gwyn@smoke.brl.mil (Doug Gwyn)
Newsgroups: comp.compression
Subject: Re: Integer not expressable in less than 13 words
Message-ID: <15901@smoke.brl.mil>
Date: 20 Apr 91 18:59:28 GMT
References: <15869@smoke.brl.mil> <1991Apr18.210832.9918@shl.com> <1991Apr19.155442.4840@looking.on.ca>
Organization: U.S. Army Ballistic Research Laboratory, APG, MD.
Lines: 19

In article <1991Apr19.155442.4840@looking.on.ca> brad@looking.on.ca (Brad Templeton) writes:
>After all, "least positive integer not expressable in less than 13
>English words"   has 11 words, so in fact there is no such animal.

But then what about the following argument:
	There are a finite (although large) number of English words.
	The number of combinations of fewer than 13 words from
	the finite set of words is also finite (although very large).
	The combinations of fewer than 13 English words that express
	positive integers form a subset of the set of all possible
	combinations of fewer than 13 English words, and thus that
	subset is finite.
	Every finite set of positive integers has a least member.
	Therefore the (finite) set of positive integers expressed by
	that subset of English word combinations has a least member.
It would seem that the phrase does describe some integer.

Yes, it's a paradox.  But it could be relevant when considering
compression schemes that encode numeric values in terms of formulas.