If you have a sequence $\displaystyle x_{n}$ and an inequality

$\displaystyle (|x_{n}|)^{\frac{1}{2}}<\beta$

Does that mean that the point to which the sequence converges (if it does) is less than $\displaystyle \beta$ or does that mean $\displaystyle (|x_{n}|)^{\frac{1}{2}}<\beta, \forall n$?