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From: phr@ucbvax.ARPA (Paul Rubin)
Newsgroups: net.math
Subject: a new (old) head-scratcher
Message-ID: <7368@ucbvax.ARPA>
Date: Wed, 22-May-85 00:21:39 EDT
Article-I.D.: ucbvax.7368
Posted: Wed May 22 00:21:39 1985
Date-Received: Thu, 23-May-85 02:54:10 EDT
Organization: University of California at Berkeley
Lines: 4

Construct a one-to-one, onto mapping between the open unit interval
(0,1) and the closed interval [0,1].  This means that every point
in (0,1) must be mapped to a unique point in [0,1] and vice versa.
It's not too hard, once you figure out the right approach.