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Ilúvatar 2019.06.17 00:14 조회 520

문제 푼 사람 0명

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

s=2^0+2^1+2^2+2^3+2^4+..................................

2s=2^1+2^2+2^3+2^4+..................................

2s+1=2^0+2^1+2^2+2^3+2^4+..................................(2^0=1)

그러므로 2s+1=s s=-1

양수를 게속 더했는데 음수가 나왔다. 이 계산에서 잘못된점은 무엇일까?

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아인수타인 Lv.12 2019.06.17 02:58

2¹=1이 아니라 2인데요?

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Ilúvatar Lv.6 2019.06.17 04:25

수정하겠습니다.

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Ilúvatar Lv.6 2019.06.18 05:33

작성자도 비밀 댓글이 안보이나요?

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- πνευμα Lv.1 2019.06.18 05:53
  
  작성자 댓글에 대댓글을 해야 보이는 걸로 알고 있습니다.
  
  원래 댓글 지우고 여기에 대댓글로 달겠습니다.
  
  좋아요0
- πνευμα Lv.1 2019.06.18 05:53 비밀댓글
  
  비밀 댓글이 등록 되었습니다!
51러 Lv.1 2019.06.18 05:58

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s= $\infty$

2s= $\infty$

2s+1=s

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- πνευμα Lv.1 2019.06.18 06:28
  
  그 일차방정식을 풀면 s=-1이 되는데, s는 양수들의 합이라는 사실과 모순이 되니까 어디가 오류인지 찾아내라는 것 같습니다.
  
  좋아요0
Ilúvatar Lv.6 2019.06.18 06:31

πνευμα님은 n이 무한이므로 무한집합끼리는 대응이 가능합니다.

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- πνευμα Lv.1 2019.06.18 06:48
  
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  $2S+1=S$ 에서 이항했을때
  
  $2S-S=-1$ 인데
  
  $2\infty - \infty=\infty - \infty$ 의 결과는 정의되지 않았기 때문에 -1이라고 단정지을수 없다-
  
  혹시 이건가요?
  
  좋아요0
Ilúvatar Lv.6 2019.06.18 07:14

πνευμα님 정답입니다.

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Ilúvatar Lv.6 2019.06.18 07:15

해결딱지 붙여주세요.

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