From: utzoo!decvax!harpo!floyd!stan
Newsgroups: net.math
Title: Re: The Funny Nature of Infinity
Article-I.D.: floyd.1131
Posted: Fri Jan 28 15:26:21 1983
Received: Sat Jan 29 04:21:22 1983
References: rabbit.1080

Referring to the note by rabbit!ss (Sharad Singhal), the points
on a line can be put into one-to-one correspondence
with the points on a plane, or area.

The only proof I can remember is one that was in Sci. Am. many years ago.
Each point is represented by real-number coordinates expressed in
decimal expansion (I know some of you doubt the validity of that, but...).

To map points on the plane into points on the line, one forms the latter's
coordinate by alternately taking digits from each of the decimal expansions
that specify the former's coordinates.

To map points on the line into points on the plane, simply reverse
the process.

		Stan King			phone: 201-386-7433
		Bell Labs, Whippany, NJ		Cornet:  8+232-7433
		room 2A-111			uucp:	 floyd!stan