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From: osman@sprite.DEC (Eric,  617 273-7484, Burlington, Ma. 01803, USA)
Newsgroups: net.math
Subject: Which has more points, the unit square, or the unit line segment ?
Message-ID: <1767@decwrl.UUCP>
Date: Mon, 22-Apr-85 17:07:31 EST
Article-I.D.: decwrl.1767
Posted: Mon Apr 22 17:07:31 1985
Date-Received: Wed, 24-Apr-85 02:57:14 EST
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I recall being told that the comparison of the size of two infinities is
resolved by finding a mapping function from one to the other.  If the
mapping function can be demonstrated to map EVERY element from the first
set onto EVERY element of the second, then the infinities are the same.

I suspect that the number of points on a line segment and a unit square
are the same.

Can anyone come up with a mapping function that maps the P in segment [0,1]
to some (X,Y) in square [(0,0),(1,1)] such that the mapping provides
complete coverage ?

If perhaps you have a mapping function that works on (0,1] or some other
variation of open/closed interval combinations, that would be fine too.

/Eric Osman, Digital, Burlington, Ma, 01803, USA