Is it true that $O(M^3 + NM^2) \, = \, O(M^3 + N)$, where $M$ and $N$ are variables of the function?
Big-oh for function of two variables
3
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computer-science
asymptotics
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3Set $M=0$; then $M^3 + NM^2$ vanishes, but $M^3 + N$ does not. – 2010-12-16
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1Technically, setting M=0 doesn't quite work, since the bound only has to hold for all M,N sufficiently large. – 2010-12-16