Editing Arithmetic progression (section)

==Intersections==
The [[Intersection (set theory)|intersection]] of any two doubly infinite arithmetic progressions is either empty or another arithmetic progression, which can be found using the [[Chinese remainder theorem]]. If each pair of progressions in a family of doubly infinite arithmetic progressions have a non-empty intersection, then there exists a number common to all of them; that is, infinite arithmetic progressions form a [[Helly family]].<ref>{{citation
 | last = Duchet
 | first = Pierre
 | editor1-last = Graham | editor1-first = R. L.
 | editor2-last = Grötschel | editor2-first = M. | editor2-link = Martin Grötschel
 | editor3-last = Lovász | editor3-first = L.
 | contribution = Hypergraphs
 | location = Amsterdam
 | mr = 1373663
 | pages = 381–432
 | publisher = Elsevier
 | title = Handbook of combinatorics, Vol. 1, 2
 | year = 1995
}}. See in particular Section 2.5, "Helly Property", [https://books.google.com/books?id=5Y9NCwlx63IC&pg=PA393 pp.&nbsp;393–394].</ref> However, the intersection of infinitely many infinite arithmetic progressions might be a single number rather than itself being an infinite progression.