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 .
References
- 1 Nathanson, Melvyn B., Elementary Methods in Number Theory^{}, Graduate Texts in Mathematics, Volume 195. Springer-Verlag, 2000.
Title | eventually coincide |
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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 |