[[집합,set]] 이론 Up: [[수학,math]] [[집합과_확률,set_and_probability]] [[집합,set]] [[이론,theory]] Sub: // [[분할,partition]]: [[집합의_분할,set_partition]] [[자연수의_분할,integer_partition]] // 이 둘은 대비됨 소박한집합론 naive_set_theory https://proofwiki.org/wiki/Definition:Naive_Set_Theory [[WpEn:Naive_set_theory]] '''Naïve set theory''' 공리적집합론 axiomatic_set_theory https://proofwiki.org/wiki/Definition:Axiomatic_Set_Theory // 이 둘도 대비됨. structural_set_theory https://ncatlab.org/nlab/show/structural+set+theory ..... 구조적집합론? 구조집합론? zeroth-order_set_theory https://ncatlab.org/nlab/show/zeroth-order+set+theory first-order_set_theory https://ncatlab.org/nlab/show/first-order+set+theory higher-order_set_theory https://ncatlab.org/nlab/show/higher-order+set+theory material_set_theory AKA membership-based set theory ex. ZFC sub - 순집합? 순수집합? [[,pure_set]] https://ncatlab.org/nlab/show/pure+set https://ncatlab.org/nlab/show/material+set+theory see also https://ncatlab.org/nlab/show/material-structural+adjunction descriptive_set_theory - 작성중 pure_set_theory pure set theory "is a system of set theory in which all elements of sets are themselves sets."(pw) https://proofwiki.org/wiki/Definition:Pure_Set_Theory ZF집합론 ZF_set_theory [[https://terms.naver.com/entry.naver?docId=4125139&cid=60207&categoryId=60207 수학백과 ZF 집합론]] ZFC집합론 ZFC_set_theory ZF s.t에 [[선택공리,choice_axiom]]을 추가한? NBG집합론 NBG_set_theory [[https://terms.naver.com/entry.naver?docId=4125138&cid=60207&categoryId=60207 수학백과 NBG 집합론]] ... Ndict:nbg+set+theory Ggl:nbg+set+theory Related: [[논리,logic]] [[사건,event]] Topics: [[reflection_principle]] - writing <> = 연산 = union $A\cup B=\left{x\middle|x\in A\textrm{ or }x\in B\right}$ intersection $A\cap B=\left{x\middle|x\in A\textrm{ and }x\in B\right}$ mutually exclusive or disjoint: $A\cap B=\not\bigcirc$ [[부분집합,subset]] complement $A^C=\left{x\middle|x\not\in A\right}$ [[교환법칙,commutativity]] $A\cap B=B\cap A$ $A\cup B=B\cup A$ [[결합법칙,associativity]] $A\cup(B\cup C)=(A\cup B)\cup C$ $A\cap(B\cap C)=(A\cap B)\cap C$ [[분배법칙,distributivity]] $A\cup(B\cap C)=(A\cup B)\cap(A\cup C)$ $A\cap(B\cup C)=(A\cap B)\cup(A\cap C)$ [[드모르간_법칙,De_Morgan_law]] { '''De Morgan's laws''' $(A\cup B)^C=A^C\cap B^C$ $(A\cap B)^C=A^C\cup B^C$ $\neg(p\wedge q)\Leftrightarrow \neg p \vee \neg q$ $\neg(p\vee q)\Leftrightarrow \neg p \wedge \neg q$ 이것은 [[논리곱]] ∧과 [[논리합]] ∨사이의 [[쌍대성,duality]].[* [[https://terms.naver.com/entry.naver?docId=3338026&cid=47324&categoryId=47324 수학백과: 부정명제]]의 3.1.] from (10개의 특강으로 끝내는 수학의 기본 원리) { ||$\sim(A\cup B)=(\sim A)\cap(\sim B)$ ||합집합의 여집합은 여집합들의 교집합이다. || ||$\sim(A\cap B)=(\sim A)\cup(\sim B)$ ||교집합의 여집합은 여집합들의 합집합이다. || } [[WpKo:드_모르간의_법칙]] [[WpEn:De_Morgan's_laws]] Up: [[명제논리,propositional_logic]], [[집합론,set_theory]] } = Bmks ko = 계승혁 - 집합과 수리논리 강의 동영상 (2020) https://www.math.snu.ac.kr/~kye/lecture_V/V_set/index.html = Bmks en = Set theory symbols https://mathvault.ca/hub/higher-math/math-symbols/set-theory-symbols/ ---- Twins: [[wiki:Google:집합론]] https://en.citizendium.org/wiki/Set_theory https://planetmath.org/settheory https://mathworld.wolfram.com/SetTheory.html https://proofwiki.org/wiki/Definition:Set_Theory https://ncatlab.org/nlab/show/set+theory https://encyclopediaofmath.org/wiki/Set_theory https://everything2.com/title/set+theory https://plato.stanford.edu/entries/set-theory/ [[Wiki:SetTheory]] [[https://terms.naver.com/entry.naver?docId=3405344&cid=47324&categoryId=47324 수학백과 집합론]]