[math-fun] Puzzle about non-empty sets

*SPOILER ALERT* For reals the smallest number is 3. Here's one set of values that works: -1, -1/phi, phi where phi = (sqrt(5)+1)/2. With rationals it can be done with 4: -2, -1/2, 1/2, 2 I'm not sure if it can be done with 3 rationals. Tom James Propp writes:

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