in the $\epsilon$-$\delta$ definition of limit,would it be wrong if the $\epsilon$ is a rational number rather than a real number?

Question

$f:E\to Y$，we write $f(x) \to q$ as $x \to p$, if

For every positive rational number $\epsilon$, there is a $\delta>0$ such that $d(f(x),q)<\epsilon$,for all points $x \in E$ for which $d(x,p)<\delta$.

Is that statement the same as the original one?