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遞移關係

子集概念嘅簡化版:已知 入面,噉如果家陣畫個新嘅波波 包住 都會喺 入面。

遞移關係粵拼dai6 ji4 gwaan1 hai6英文transitive relation)係邏輯學上嘅一個概念。想像有 3 件物件 ABC,如果「ABR 嘅關係」而且「BCR 嘅關係」必定表示「AC 會成 R 嘅關係」,噉 R 就算係一段遞移關係。

基本定位

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呢幅圖入面嘅 垂直-兩條線相交嗰點形成兩個直角

想像而家有隻關係 ,如果話 具有遞移呢種特性,即係話[1][2]

  • 只要 呢兩句陳述式成立,就表示
  • 包保會成立。

當中 係某啲變數

舉兩個具體例子說明,

  1. 等如就係一種遞移關係,設 3 個數 ,如果 成立,「」都包保實會成立;
  2. 幾何學上講嘅垂直就係唔遞移(intransitive),如果
    呢兩條直線成垂直,而且
    呢兩條直線又成垂直,
    -噉 實唔會成垂直。

遞移關係唔使一定係講數學或者邏輯,例如「係... 嘅阿爸」就係一段唔遞移關係[1]

  • 已知阿偉係明仔嘅阿爸,
  • 又已知阿發係阿偉嘅阿爸,
  • 噉阿發應該會係明仔嘅阿爸(而會係明仔嘅阿爺)。

常見關係

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以下呢啲關係都係遞移嘅:

... 呀噉。

睇埋

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  • 理性選擇理論:廿世紀嗰陣嘅經濟學,成日都會將人當做完美理性決策者,認為人做經濟決策嗰時會喺入面同每個選項計個數,精確噉表示嗰個選項「有幾正」;如果呢個諗法係真確偏好呢家嘢就應該會係遞移嘅-如果一個人鍾意選項 A 多過鍾意選項 B 而同時又鍾意選項 B 多過鍾意選項 C,噉佢理應會鍾意選項 A 多過鍾意選項 C(諗法作出嘅預測),不過實證嘅研究表明,呢個預測成立[4][5]

來源

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  1. 1.0 1.1 transitive law. Encyclopedia Britannica.
  2. Smith, Douglas; Eggen, Maurice; St.Andre, Richard (2006), A Transition to Advanced Mathematics (6th ed.), Brooks/Cole.
  3. MHF 3202 (Larson) Subset relation is transitive (PDF).
  4. Nishimura, H., & Ok, E. A. (2016). Utility representation of an incomplete and nontransitive preference relation. Journal of Economic Theory, 166, 164-185.
  5. Nishimura, H. (2018). The transitive core: Inference of welfare from nontransitive preference relations (PDF). Theoretical Economics, 13(2), 579-606.

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遞移關係
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