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In mathematics, an IP set is a set of natural numbers which contains all finite sums of some infinite set. The finite sums of a set D of natural numbers are all those numbers that can be obtained by adding up the elements of some finite nonempty subset of D.The set of all finite sums over D is often denoted as FS(D). Slightly more generally, for a sequence of natural numbers (ni), one can consider the set of finite sums FS((ni)), consisting of the sums of all finite length subsequences of (ni).

Attributes	Values
rdfs:label	IP-Menge (de) IP set (en)
rdfs:comment	In der Mathematik bezeichnet der Begriff IP-Menge eine Menge natürlicher Zahlen, die alle endlichen Summen einer unendlichen Menge von natürlichen Zahlen enthält. Die Bezeichnung IP-Menge (IP-set) geht auf Hillel Fürstenberg und zurück; IP steht dabei für „Infinite-dimensional Parallelepiped“. (de) In mathematics, an IP set is a set of natural numbers which contains all finite sums of some infinite set. The finite sums of a set D of natural numbers are all those numbers that can be obtained by adding up the elements of some finite nonempty subset of D.The set of all finite sums over D is often denoted as FS(D). Slightly more generally, for a sequence of natural numbers (ni), one can consider the set of finite sums FS((ni)), consisting of the sums of all finite length subsequences of (ni). (en)
dcterms:subject	Semigroup theory Ramsey theory Ergodic theory
Wikipage page ID	3999498 (xsd:integer)
Wikipage revision ID	1118152741 (xsd:integer)
Link from a Wikipage to another Wikipage	Non-empty set Benjamin Weiss Infinite set Semigroup theory Mathematics Piecewise syndetic set Ergodic Ramsey theory Syndetic set Semigroup Parallelepiped Journal of Combinatorial Theory Ultrafilter Hillel Furstenberg Ramsey theory Ergodic theory Thick set Natural number Ramsey's theorem Vitaly Bergelson Milliken–Taylor theorem Partition regular dbr:Neil_Hindman
Link from a Wikipage to an external page	http://home.hia.no/~ingerjh/forskning/bhm2jun03.pdf http://nhindman.us/research/large.pdf https://web.archive.org/web/20061117184558/http:/www.mtholyoke.edu/~jmcleod/somenotionsofsize.pdf http://www.math.ohio-state.edu/~vitaly/vbkatsiveli20march03.pdf
sameAs	IP set IP set IP set IP set
dbp:wikiPageUsesTemplate	dbt:Citation_style dbt:Cite_journal dbt:Reflist
has abstract	In der Mathematik bezeichnet der Begriff IP-Menge eine Menge natürlicher Zahlen, die alle endlichen Summen einer unendlichen Menge von natürlichen Zahlen enthält. Die Bezeichnung IP-Menge (IP-set) geht auf Hillel Fürstenberg und zurück; IP steht dabei für „Infinite-dimensional Parallelepiped“. (de) In mathematics, an IP set is a set of natural numbers which contains all finite sums of some infinite set. The finite sums of a set D of natural numbers are all those numbers that can be obtained by adding up the elements of some finite nonempty subset of D.The set of all finite sums over D is often denoted as FS(D). Slightly more generally, for a sequence of natural numbers (ni), one can consider the set of finite sums FS((ni)), consisting of the sums of all finite length subsequences of (ni). A set A of natural numbers is an IP set if there exists an infinite set D such that FS(D) is a subset of A. Equivalently, one may require that A contains all finite sums FS((ni)) of a sequence (ni). Some authors give a slightly different definition of IP sets: They require that FS(D) equal A instead of just being a subset. The term IP set was coined by Hillel Furstenberg and Benjamin Weiss to abbreviate "infinite-dimensional parallelepiped". Serendipitously, the abbreviation IP can also be expanded to "idempotent" (a set is IP if and only if it is a member of an idempotent ultrafilter). (en)
gold:hypernym	Set
prov:wasDerivedFrom	wikipedia-en:IP_set?oldid=1118152741&ns=0
page length (characters) of wiki page	6031 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:IP_set
is Link from a Wikipage to another Wikipage of	List of exceptional set concepts Piecewise syndetic set Ergodic Ramsey theory Partition regularity Hillel Furstenberg Milliken–Taylor theorem Slicing the Truth Hindman's theorem Hindman’s theorem
is Wikipage redirect of	Hindman's theorem Hindman’s theorem
is known for of	Hillel Furstenberg
is known for of	Hillel Furstenberg
is foaf:primaryTopic of	wikipedia-en:IP_set

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