분배법칙,distributivity

distributivity 분배성, distributive property 분배 성질, distributive law 분배 법칙
분배법칙, 배분법칙

See also 체,field

일반적인 algebra(대수학,algebra)에선
a * (b + c) = (a*b) + (a*c)는 성립하지만
a + (b * c) = (a+b) * (a+c)는 아님!
But..
불_대수,Boolean_algebra 불_논리,Boolean_logic에서 and와 or은 서로 분배법칙을 만족? CHK
a or (b and c) == (a or b) and (a or c)
a and (b or c) == (a and b) or (a and c)



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1. 분배법칙의 확장

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2. left distributive vs. right distributive

왼쪽 분배 vs 오른쪽 분배?

left distributive:
z·(x + y) = z·x + z·y
right distributive:
(x + y)·z = x·z + y·z

다를 수도 있다, chk. 정확히 언제? 가환성(curr 교환법칙,commutativity)이 없을 때?
... Ggl:left distributive right distributive

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3. Σ의 (이른바) '분배법칙'?

$\sum_{i}(pa_i+qb_i)=p\sum_{i}a_i+q\sum_{i}b_i$
이것은 확률변수,random_variable의 평균, 분산 등을 계산할 때 쓰임

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4. REL

관련:
이항연산,binary_operation
distributivity는 이항연산 한 가지에 대한 연산의 성질인 교환성/결합성(curr. pages 교환법칙,commutativity, 결합법칙,associativity)과 달리 이항연산,binary_operation 두 가지에 대한? chk
그리고 그 둘의 순서가 중요 - 맨 위에 쓴 바와 같이.

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5. MKL


completely_distributive_lattice - w
completely distributive lattice
https://encyclopediaofmath.org/wiki/Completely_distributive_lattice
https://ncatlab.org/nlab/show/completely distributive lattice
complete_lattice and distributive_lattice ? chk

lattice { 격자,lattice or 래티스,lattice - cur. RR 래티스,lattice }
WtEn:lattice#Noun
7 "A partially ordered set(부분순서집합,partially_ordered_set,poset) in which every pair of elements has a unique 상한,supremum and a unique 하한,infimum."
lattice_theory
WtEn:lattice_theory




AKA (드물게) 배분법칙(다만 배분은 보통 allocation.)
상위: 산술,arithmetic 대수학,algebra

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