About: Large set (combinatorics)

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In combinatorial mathematics, a large set of positive integers is one such that the infinite sum of the reciprocals diverges. A small set is any subset of the positive integers that is not large; that is, one whose sum of reciprocals converges. Large sets appear in the Müntz–Szász theorem and in the Erdős conjecture on arithmetic progressions.

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rdf:type	yago:Abstraction100002137 yago:Arrangement107938773 yago:Group100031264 yago:Ordering108456993 yago:WikicatIntegerSequences yago:Sequence108459252 yago:Series108457976
rdfs:label	Large set (combinatorics) (en) Small set (組み合わせ論) (ja) 倒數和發散 (zh)
rdfs:comment	In combinatorial mathematics, a large set of positive integers is one such that the infinite sum of the reciprocals diverges. A small set is any subset of the positive integers that is not large; that is, one whose sum of reciprocals converges. Large sets appear in the Müntz–Szász theorem and in the Erdős conjecture on arithmetic progressions. (en) 数学における組合せ論において small set は自然数の集合で、次の級数が収束するもののことである。large setとは、それ以外の集合(すなわち、件の級数が発散するもの)のことである。 (ja) 数学中，倒數和發散的正整數集是元素倒數的級數和發散的集合，即滿足下文簡稱「大集」。與之相反，倒數和收斂的集合，元素倒數和有限，下文簡稱「小集」。如此區分集合的大小，見於和埃尔德什等差数列猜想。 (zh)
dcterms:subject	Combinatorics Integer sequences Mathematical series
Wikipage page ID	3152856 (xsd:integer)
Wikipage revision ID	1119365137 (xsd:integer)
Link from a Wikipage to another Wikipage	Prime power Proof that the sum of the reciprocals of the primes diverges Basel problem Decimal List of sums of reciprocals Paul Erdős Uniform norm Powerful number Continuous function Geometric progression Convergent series Erdős conjecture on arithmetic progressions Stone–Weierstrass theorem Combinatorics Dense set Harmonic series (mathematics) Perfect power Müntz–Szász theorem Brun's constant Twin prime Divergent series Analytic number theory Combinatorics Integer sequences Numeral system Kempner series Mathematical series Prime number Arithmetic progression 2 Polynomial Positive integer Square number Ideal (set theory) Asymptotic density Union (set theory) Subset Erdős conjectures Infinite sum Cube number
sameAs	Large set (combinatorics) Large set (combinatorics) Large set (combinatorics) Large set (combinatorics) Large set (combinatorics) Large set (combinatorics)
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has abstract	In combinatorial mathematics, a large set of positive integers is one such that the infinite sum of the reciprocals diverges. A small set is any subset of the positive integers that is not large; that is, one whose sum of reciprocals converges. Large sets appear in the Müntz–Szász theorem and in the Erdős conjecture on arithmetic progressions. (en) 数学における組合せ論において small set は自然数の集合で、次の級数が収束するもののことである。large setとは、それ以外の集合(すなわち、件の級数が発散するもの)のことである。 (ja) 数学中，倒數和發散的正整數集是元素倒數的級數和發散的集合，即滿足下文簡稱「大集」。與之相反，倒數和收斂的集合，元素倒數和有限，下文簡稱「小集」。如此區分集合的大小，見於和埃尔德什等差数列猜想。 (zh)
prov:wasDerivedFrom	wikipedia-en:Large_set_(combinatorics)?oldid=1119365137&ns=0
page length (characters) of wiki page	4755 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Large_set_(combinatorics)
is Link from a Wikipage to another Wikipage of	List of sums of reciprocals Erdős conjecture on arithmetic progressions Størmer number Cluster prime Müntz–Szász theorem Small set (combinatorics) Large set
is Wikipage redirect of	Small set (combinatorics)
is foaf:primaryTopic of	wikipedia-en:Large_set_(combinatorics)

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