Use of Big $O$ notation in a particular situation
Suppose we have $$ a \cdot \left(1+O\left(\frac
xy\right)\right)=O\left(z\right). $$ I wonder if it is possible to obtain
an asymptotic expansion of $a$ in terms of $x$, $y$ and $z$. Since both
sides are actually sets, I have no idea on how to deal with this
situation. Thank you!
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