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eventually coincide
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(Definition)
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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 equivalence of sets when dealing with asymptotic
properties such as density.
- 1
- Nathanson, Melvyn B., Elementary Methods in Number Theory, Graduate Texts in Mathematics, Volume 195. Springer-Verlag, 2000.
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"eventually coincide" is owned by mathcam.
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| Other names: |
eventually coinciding |
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Cross-references: properties, equivalence relation, relation, integers
There is 1 reference to this entry.
This is version 2 of eventually coincide, born on 2005-03-26, modified 2005-04-05.
Object id is 6907, canonical name is EventuallyCoincide.
Accessed 2150 times total.
Classification:
| AMS MSC: | 11B13 (Number theory :: Sequences and sets :: Additive bases) |
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Pending Errata and Addenda
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