  Plotting $({\zeta},U(x,y),V(x,y),x,y,z)$ and numerical calculations show that
${\zeta}(s)=0$ finitely many times in the Interval $I$ with $k$ roots in the
interval all of which are on the critical line which proves the Riemann
Hypothesis in $I$. It is shown by using groups of intervals how to extend the
proof of the Riemann Hypothesis in $I$ to intervals at infinity which extends
the proof of the Riemann Hypothesis from the finite domain in the critical
strip to the entire critical strip.
