From: utzoo!decvax!yale-com!leichter Newsgroups: net.math Title: Re: touching Article-I.D.: yale-com.734 Posted: Wed Jan 26 21:30:53 1983 Received: Sun Jan 30 09:18:45 1983 References: ihlpb.274 ...all of which illustrates once again why mathematics exists. If you insist on using vague English descriptions "touching" "occupying the same space" etc. you will easily produce contradictions. So what? Phrase this rigorously and STILL find a contradiction, and you might have something there. 'Till then...consider the following "proof". Thm: A ham sandwich is better than complete happiness in life. Pf: Everyone will agree that nothing is better than complete happiness in life. On the other hand, a ham sandwich is better than nothing. Hence, by the transitivity of "better than", we have our theorem. QED -- Jerry decvax!yale-comix!leichter