V2EX residue class

Residue Class

释义 Definition

剩余类 / 同余类:在模 \(n\) 的意义下,所有与某个整数 \(a\) 同余(即相差 \(n\) 的倍数)的整数所组成的集合,记作 \([a]\) 或 \(a \bmod n\)。常见于数论与抽象代数。
(在更一般的代数语境中,也可指“等价类”。)

发音 Pronunciation (IPA)

/rzdu kls/

例句 Examples

All integers that differ by a multiple of 5 belong to the same residue class modulo 5.
所有相差 5 的倍数的整数都属于模 5 的同一个剩余类。

In modular arithmetic, the residue class of 7 mod 3 is the same as the residue class of 1 mod 3, because 7 ≡ 1 (mod 3).
在模运算中,7 在模 3 下的剩余类与 1 的剩余类相同,因为 7 ≡ 1(mod 3)。

词源 Etymology

residue 源自拉丁语 residuum,意为“剩下的东西、残余”;class 表示“类别、群体”。合起来表示“由同余关系划分出来的一个‘剩余’类别”,即把整数按除以 \(n\) 后的“余数意义”分组得到的集合。

相关词 Related Words

文学与经典著作 Literary Works

  • Jean-Pierre Serre, A Course in Arithmetic(《算术教程》)
  • G. H. Hardy & E. M. Wright, An Introduction to the Theory of Numbers(《数论导引》)
  • David S. Dummit & Richard M. Foote, Abstract Algebra(《抽象代数》)
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