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 $n\ge C$. 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 .

Title	eventually coincide
Canonical name	EventuallyCoincide
Date of creation	2013-03-22 15:09:30
Last modified on	2013-03-22 15:09:30
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	5
Author	mathcam (2727)
Entry type	Definition
Classification	msc 11B13
Synonym	eventually coinciding