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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  • 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)
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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. (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)
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  • Large set (combinatorics) (en)
  • Small set (組み合わせ論) (ja)
  • 倒數和發散 (zh)
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