to the Dirichlet eta function (s)=\_[u=1]{}\^ . \[Riemann\_eta\] It has been shown for the Riemann zeta function that it has trivial zeros at the points $-2,-4,\dots$ It is also known that any non-trivial zero lies in the complex set $\{s : 0 < \Re(s) < 1 \}$, called the critical strip. The complex set $\{s :   \Re(s) =1/2 \}$ is called the critical line. The Riemann Hypothesis asserts that any non-trivial zero $s$ has the real part $\Re(s) = 1/2$, i.e., lies on the critical line.

This problem has been of central interest to mathematicians for a long time and many unsuccessful attempts have been made to either prove or disprove it. Since both the Riemann zeta function and the Dirichlet eta function are defined as sums of the infinite number of items, in this paper, we look at them and at the Riemann Hypothesis using a new approach to infinity introduced in [@Sergeyev; @www; @informatica; @first; @Lagrange]. This approach, in particular, incorporates the following two ideas.

i\) The point of view on infinite and infinitesimal quantities applied in this paper uses strongly two methodological ideas borrowed from the modern Physics: relativity and interrelations holding between the object of an 