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함께 풀고 싶은 문제

창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.

[창의 퍼즐] [0.999...]=0 or 1 (수학 토론)

리프 2020.03.09 13:31 조회 745

문제 푼 사람 0명

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

수학 관련 토론인데 한 번 테스트용으로 올려봤고 만약 반응 좋으면 앞으로도 계속 수학 토론에 대해서 올릴 예정입니다.

1) 0.999...의 값이 1이 됨을 보이시오. (귀찮으면 안하셔도 됩니다.)

2) [0.999...]=0일까 1일까? (단, [x]란 x를 넘지 않는 최대 정수, 즉 x의 정수부분을 의미한다.)

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K→C≡N Lv.11 2020.03.09 16:32

1.0.9999999999999999999999999999999................는 1이 아니다!

1과 무한히 가까워 질 뿐, 1이 될 수 없다.반비례그래프가 0과 무한히 가까워지지만 0이 될 수 없는것과 마찬가지인것이다.

그러므로 [0.9999999999999999999999999]는 0이다.

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- 21세기오일러 Lv.11 2020.03.09 17:14
  
  저는 0.999...은 1이라 생각합니다. 0.999...을 x라 놓으면
  
  10x=9.999...
  
  10x-x=9.999...-0.999
  
  9x=9
  
  x=1이기 때문입니다
  
  좋아요0
- † J.H † Lv.9 2020.03.09 17:57
  
  0.9999999999999는 1아닌가요?
  
  좋아요0
- 리프 Lv.7 2020.03.10 05:25
  
  http://www.polymath.co.kr/contents/view/10551
  
  추가질문에 답해주시면 감사하겠습니다.
  
  좋아요0
21세기오일러 Lv.11 2020.03.09 17:15

2번은 좀 애매한데 저는 1이라 생각합니다. 0.999...=1이기 때문이죠 단지 표현 방식이 다른 것 뿐

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- 리프 Lv.7 2020.03.10 05:25
  
  http://www.polymath.co.kr/contents/view/10551
  
  추가질문에 답해주시면 감사하겠습니다.
  
  좋아요0
sicma Lv.11 2020.03.09 18:10

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1번. $\lim_{n\rightarrow \infty}\frac{10^{n}-1}{10^{n}}$ 이므로 로피탈의 정리를 쓰면 1이네요.

2번은 1이라고 생각해요 1을 다르게 쓴다고 해서 0이 되는 것은 아니니까요..

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- 리프 Lv.7 2020.03.10 05:25
  
  http://www.polymath.co.kr/contents/view/10551
  
  추가질문에 답해주시면 감사하겠습니다.
  
  좋아요0
피타구라스 Lv.9 2020.03.09 20:03

0.9999....는 순환소수로 생각해보면9/9=1이 되기 때문에 1이 아닐까요?

댓글 작성하기 좋아요0 댓글수1
- 리프 Lv.7 2020.03.10 05:25
  
  http://www.polymath.co.kr/contents/view/10551
  
  추가질문에 답해주시면 감사하겠습니다.
  
  좋아요0
아인수타인 Lv.12 2020.03.09 21:53

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Line: 558
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/4096fd3884e6322476b4a1610fded6f9.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/4096fd3884e6322476b4a1610fded6f9.gif): Failed to open stream: Operation not permitted

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

1번은 1이라고 생각합니다. 왜냐하면 $\frac{1}{3}=0.33333\cdot \cdot \cdot$ 이고 양변에 3을 곱하면 $1=0.99999\cdot \cdot \cdot$ 이기 때문입니다.

2번 역시 1이라고 생각합니다. 왜냐하면 단지 표현법만 다른 것이기 때문입니다.

댓글 작성하기 좋아요0 댓글수1
- 리프 Lv.7 2020.03.10 05:25
  
  http://www.polymath.co.kr/contents/view/10551
  
  추가질문에 답해주시면 감사하겠습니다.
  
  좋아요0