V2EX supremum

Supremum

定义 Definition

supremum(上确界):在数学(尤其是实分析与序理论)中,指一个集合的最小上界也就是所有上界里“最小的那个”。它不一定属于该集合。(常与 infimum“下确界”相对;在日常英语中较少使用。)

发音 Pronunciation

/suprmm/

例句 Examples

The supremum of the set is 1.
这个集合的上确界是 1。

Although the sequence never reaches 1, its supremum is still 1 because the terms can get arbitrarily close to it.
尽管这个序列永远达不到 1,但它的上确界仍然是 1,因为它的项可以无限接近 1。

词源 Etymology

来自拉丁语 supremus(“最高的、最上的”)的中性形式,带有“最高点/上界”的含义;在数学语境中发展为“上确界(最小上界)”这一严格定义。

相关词 Related Words

文学与著作 Literary Works

  • Walter Rudin, Principles of Mathematical Analysis(《数学分析原理》)
  • H. L. Royden & P. M. Fitzpatrick, Real Analysis(《实分析》)
  • Tom M. Apostol, Mathematical Analysis(《数学分析》)
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