There are many such sets of size 3; just look at the intersection of the surfaces xyz = 1 and x+y+z = 0. E.g., {2^(2/3), -2^(-1/3), -2^(-1/3)} —Dan -----Original Message-----

From: James Propp <jamespropp@gmail.com>

The sum of the elements of the empty set is 0; the product of the elements of the empty set is 1.

What is the smallest non-empty set of real numbers that shares this property with the empty set?

(What if we require all the numbers to be rational? I haven't figured this part out yet.)

Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun