eventually coincide

Let $A$ and $B$ be two nonempty sets of integers. We say that $A$ and $B$ eventually coincide if there is an integer $C$ such that $n\in A$ if and only if $n\in B$ for all $n\geq C$. In this case, we write $A\sim B$, noting that the relation of eventually coinciding is clearly an equivalence relation. While a seemingly trivial notation, this turns out to be the “right” notion of of sets when dealing with asymptotic properties such as .

References

Title eventually coincide EventuallyCoincide 2013-03-22 15:09:30 2013-03-22 15:09:30 mathcam (2727) mathcam (2727) 5 mathcam (2727) Definition msc 11B13 eventually coinciding