V2EX surjective

Surjective

释义 Definition

(数学)满射的;满的。指一个函数/映射把值域覆盖整个陪域:对陪域中的每个元素,都至少有一个定义域中的元素映到它(也常说“onto”)。

发音 Pronunciation

/srdk.tv/

例句 Examples

A surjective function hits every value in its codomain.
满射函数会取到它陪域中的每一个值。

The mapping is surjective, so for any \(y\) in the codomain there exists an \(x\) such that \(f(x)=y\).
该映射是满射,因此对陪域中的任意 \(y\),都存在某个 \(x\) 使得 \(f(x)=y\)。

词源 Etymology

surjective 来自现代数学术语,构词上与 injective(单射)bijective(双射) 相呼应;其核心含义是“向上/覆盖到(onto)”,强调函数把输出“覆盖”到整个陪域。该词在 20 世纪数学写作中逐渐固定为标准用语。

相关词 Related Words

文学与经典著作 Literary Works

  • Algebra Serge Lang
  • Category Theory for the Working Mathematician Saunders Mac Lane
  • Principles of Mathematical Analysis Walter Rudin
  • Topology James R. Munkres
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