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From: colonel@gloria.UUCP (Col. G. L. Sicherman)
Newsgroups: net.math
Subject: Re: (0,1) -> [0,1] ?  No, congruence.
Message-ID: <780@gloria.UUCP>
Date: Mon, 27-May-85 23:07:20 EDT
Article-I.D.: gloria.780
Posted: Mon May 27 23:07:20 1985
Date-Received: Thu, 30-May-85 04:07:14 EDT
References: <376@h-sc1.UUCP> <140@harvard.ARPA>
Organization: SUNY-Buffalo Computer Sci.
Lines: 10

> Problem: map (0,1) to [0,1] bijectively.
> Solution: choose some ordering of ANY countable subset of (0,1).  Map
>   the first and second elements to 0 and 1.  Map the nth element to the
>   n-2nd element.  Leave everything else alone.

That reminds me of a classic problem of Sierpinski's: find a bounded
set in the plane that's congruent (geometrically) to itself minus one point.
-- 
Col. G. L. Sicherman
...{rocksvax|decvax}!sunybcs!colonel