V2EX infimum

Infimum

释义 Definition

(数学)下确界:在一个集合的所有下界中最大的那个下界。若某数 \(m\) 是集合的下确界,表示 \(m\) 不一定属于该集合,但集合中所有元素都不小于 \(m\),并且任何比 \(m\) 更大的数都不再是下界。

发音 Pronunciation (IPA)

/nfmm/

例句 Examples

The infimum of the set is 0.
这个集合的下确界是 0。

In real analysis, proving that a nonempty set bounded below has an infimum is a key step in many arguments.
在实分析中,证明一个非空且有下界的集合存在下确界,是许多论证中的关键步骤。

词源 Etymology

infimum 来自拉丁语 infimus(“最低的、最下的”),是 inferus(“下方的”)的最高级形式之一;在数学语境中借用来表示“最下端”的界限,即“下确界”。对应地,supremum(上确界)来自拉丁语 supremus(“最高的”)。

相关词 Related Words

文学与经典用例 Literary Works

  • Principles of Mathematical Analysis(Walter Rudin,《数学分析原理》)
  • Real Analysis: Modern Techniques and Their Applications(Gerald B. Folland,《实分析》)
  • Real and Complex Analysis(Walter Rudin,《实与复分析》)
  • Introduction to Real Analysis(Robert G. Bartle & Donald R. Sherbert,《实分析导论》)
  • Measure Theory(Paul R. Halmos,《测度论》)
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