Bivalent BAM theorem Suppose AS;(x;)>0 Then AS;(x)=S;()-S;(x) =1-0 This implies so the product is positive: △S,(x,)[x+1-U,]>0 Another case suppose AS;(x;)<0 △S,(x)=S,(x,k+1)-S,(x,) =0-1 99 Bivalent BAM theorem Suppose Si (xi )  0 ( ) ( ) ( ) k i i k i i i i S x = S x − S x +1 = 1− 0 Then This implies so the product is positive: i k xi U +1 0 1  −  + ( )[ ] i k Si xi xi U Another case suppose Si (xi )  0 ( ) ( ) ( ) k i i k i i i i S x = S x − S x +1 = 0 −1