Question

If 0>x>y, 0>z>w then prove 0<xz<yw​

Answer 1

Answer:

The base case is x<y. Then x+m=y where m>0.

Then assume xk<yk. Then xk+n=yk and n>0.

Then xk+x+m+n=y+yk

or x(k+1)+(m+n)=y(k+1)

Thus x(k+1)<y(k+1).

Thus xz<yz for all z∈N.