수학동아 - 폴리매스

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자유게시판

수학을 주제로 떠들어 보세요!

[수학 정보] 연속된 곱

delta 2019.12.08 08:31 조회 1043

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

$S = [a,b]$ 일때,

$\prod S = \left\{ \begin{matrix} 0& ext{if} & 0\in S\\ 1& ext{if} &a= frac{1}{b}>0 \\ \infty & ext{if} & a> frac{1}{b}>0\\ 0 & ext{if} & frac{1}{b}>a>0\\ -1 & ext{if} & -1> frac{1}{b}=a\\ -\infty & ext{if} & -1> frac{1}{b}>a\\ 0 & ext{if} & -1>a> frac{1}{b} \end{matrix}\right.$

입니다.

저 식은 $S = (a,b)$ 일때도 성립합니다.

이전글 암산꿀팁

다음글 lim x->0 sinx/x =1의 간단한 증명(기하학적 증명?)

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K→C≡N Lv.11 2019.12.08 17:02

무슨말인지 못알아듣겠는 인간.

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21세기오일러 Lv.11 2019.12.08 20:37

못 알아듣고 있는 2인

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리프 Lv.7 2019.12.10 03:10

무슨 뜻인지는 알겠는데 무한집합의 모든 원소를 곱한다는 것이 수학적으로 정의하는 것이 가능한지 모르겠네요..(+곱하는 순서를 역수끼리 곱하도록 바꾼 후 곱해서 저런 결과가 나온 것 같은데 무한히 많은 원소에 대해 연산을 할 때는 순서를 함부로 바꾸면 안 될 껄요)

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- 디듀우 Lv.7 2019.12.22 04:50
  
  굳이 순서를 안바꿔도 역수로 약분되는건 사실이니까 맞지 않을까요?
  
  좋아요0
은총알 Lv.11 2019.12.11 09:26

못 알아듣는 死인

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mathwizard Lv.7 2019.12.12 05:13

무슨 말씀이신지...

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조곰팅 Lv.5 2019.12.15 20:09

이해만 되는 1인

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수포자 Lv.6 2020.01.02 05:45

못 알아듣겠는 5인(맞나?)

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황금 열쇠 Lv.7 2020.01.24 02:08

못 알아듣는 6인

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아루키데메스 Lv.5 2020.05.30 07:39

못 알아듣겠다는 7인...

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