Quote by WACG
I am puzzled by the following infinite product:
Let B > A
A  B = [A^(1/2) + B^(1/2)] * [A^(1/2)  B^(1/2)]
= [A^(1/2) + B^(1/2)] * [A^(1/4) + B^(1/4)] * [A^(1/4)  B^(1/4)]
=[A^(1/2) + B^(1/2)] * [A^(1/4) + B^(1/4)] * [A^(1/8) + B^(1/8)] * [A^(1/8)  B^(1/8)]
etc.
Continuing the obvious expansion into an infinite product produces a sequence of terms none of which are negative. However, since B > A then A  B is a negative value. How can a infinite product of terms greater than zero produce a negative value? Surely there is a "simple" explanation.
Thanks for any comments.

In each of the products the last term to the right is negative.