Can we deduce that the equation $f(x)=?iso-8859-1?Q?=3D0$_has_finite_number_of_solutions_in_the_interval_$?=(-‡,2)$=?iso-8859-1?Q?$(-=81=87=2C2?=)$=?iso-8859-1?Q?=3F?=

Can we deduce that the equation $f(x)=0$ has finite number of solutions in
the interval $(-‡,2)$?

Let us consider an equation $f(x)=0$ where $f$ is a real analytic
function. Assume that this equation has still a finite number of solutions
in any interval of the form $(y,2)$ where the number $y<2$ is located in
an infinite discrete set. Can we deduce that the equation $f(x)=0$ has
finite number of solutions in the interval $(-‡,2)$