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- matematický vztah popisující velikost sjednocení množin (cs)
- 組合數學的計數技巧，重複數算的數目要扣除 (zh)
- counting technique in combinatorics (en)
- identità matematica (it)
- kombinatorikai leszámlálási technika (hu)
- עיקרון קומבינטורי במתמטיקה בדידה ותורת הקבוצות (iw)
- técnica de contagem em combinatória (pt)
- Technik zur Bestimmung der Mächtigkeit einer mathematischen Menge (de)
- técnica de contaxe que xeneraliza o método familiar de obter o número de elementos na unión de dous conxuntos finitos (gl)
- równanie będące twierdzeniem kombinatoryki i częścią definicji w teorii miary (pl)
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- 2803 (xsd:integer)
- p/i050430 (en)
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- Substitute
on the right hand side of . Notice that appears once on both sides of . So we must show that for all with , the terms cancel out on the right hand side of . For that purpose, take a fixed such that and take an arbitrary fixed such that .
Notice that must be a set for each positive or negative appearance of on the right hand side of that is obtained by way of the multiset such that . Now each appearance of on the right hand side of that is obtained by way of such that is a set that contains cancels out with the one that is obtained by way of the corresponding such that is a set that does not contain . This gives the desired result. (en)
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- Proof of (en)
- Inclusion-and-exclusion principle (en)
- principle of inclusion–exclusion (en)
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- Inclusion–exclusion principle (en)
- Principi d'inclusió-exclusió (ca)
- Princip inkluze a exkluze (cs)
- Inkluziveco-ekskluda principo (eo)
- Prinzip von Inklusion und Exklusion (de)
- Bilketa (probabilitatea) (eu)
- Principio de inclusión-exclusión (es)
- Principe d'inclusion-exclusion (fr)
- Principio di inclusione-esclusione (it)
- 包除原理 (ja)
- 포함배제의 원리 (ko)
- Zasada włączeń i wyłączeń (pl)
- Principe van inclusie en exclusie (nl)
- Princípio da inclusão-exclusão (pt)
- Формула включений-исключений (ru)
- Principen om inklusion/exklusion (sv)
- Формула включень-виключень (uk)
- 排容原理 (zh)
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