Here $O$ means BIG-O. https://en.wikipedia.org/wiki/Big_O_notation
If i am given with some data such that $$\|y_{\alpha}-x\| \leq O(\alpha^{\mu}) + O(\alpha^{\eta})$$ where $y$ is some variable depending on $\alpha$, and $\mu , \eta \in \mathbb{R^+}$ Such that $\mu < \eta$. Here limit in definition of $O$ is taken as $\alpha \to 0$. Then can i write $$\|y_{\alpha}-x\| \leq O(\alpha^{\mu}) $$ Is it correct or not?
According to me it is correct as $\alpha^{\eta} < \alpha ^{\mu}$ as $\alpha \to 0$.