An elementary and real approach to values of the Riemann zeta function

An elementary approach for computing the values at negative integers of the Riemann zeta function is presented. The approach is based on a new method for ordering the integers and a new method for summation of divergent series. We show that the values of the Riemann zeta function can be computed, without using the theory of analytic continuation and functions of complex variable.
Comment: added comments on zeroes of $\eta(s)$ on page 3 and some new refs