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