From: utzoo!decvax!harpo!ihnp4!ihuxe!aark
Newsgroups: net.math
Title: The Funny Nature of Infinity
Article-I.D.: ihuxe.193
Posted: Wed Jan 26 12:21:35 1983
Received: Sat Jan 29 07:12:02 1983
Reply-To: aark@ihuxe.UUCP (Alan R. Kaminsky)


Infinity is a funny thing.

Consider two infinite sets: the set of nonnegative integers and the set
of all integers.  The first set is a subset of the second, and one would
think that the first set is half as large, whatever that means, as the
second set.  Actually, the two sets are exactly the same size.  More
rigorously, the members of the two sets can be put into one-to-one
correspondence.

One would also intuitively think that there are many more rational
numbers (the set of all numbers that can be expressed as the ratio of
two integers) than there are nonnegative integers.  Wrong again: these
two sets are also the same size (can be put into one-to-one correspondence).

Infinity is a funny thing.

Alan R. Kaminsky
Bell Laboratories, Naperville, IL
...ihnp4!ihuxe!aark