We are in ZFC & CH. Given family $Y=\{y_\alpha\}_{\alpha<\omega_1}$ of infinitesimal $\omega$-sequences of rational numbers with the property: $\forall\alpha<\beta: \lim_{n\to\infty}\frac{y_{\beta n}}{y_{\alpha n}}=0$. Can we prove that for any infinitesimal sequence $y$ there exists $y_\alpha$ such that $\lim_{n\to\infty}\frac{y_{\alpha n}}{y_{n}}=0$?