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[수학 정보] 1 / 0 * 0?
ALPACA 2020.09.13 21:02 조회 849
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1 / 0은 무한 입니다. 1 / n * n은 1입니다. 그런데 1 / 0 * 0은 얼마인가요?

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  •  
    리퍼 Lv.6 2020.12.15 23:15

    모든 수가 가능합니다.

    (먼저 설명하자면, 0 / 0은 모든 수가 가능하며, 불가능한 식이 아닙니다.)

    1 / 0 * 0에서 순서를 조금 바꾸면

    0 / 0 * 1이 됩니다. (순서를 바꿔도 결과는 달라지지 않습니다.)

    이 때 0 / 0은 위에서 말했듯이 모든 수가 가능하며, 여기서 * 1을 해도 결과는 바뀌지 않습니다.

     

    *참고 0 / 0이 모든 수가 가능함을 증명

    0 / 0 = n이라고 할 때

    나누기 0을 이항하면

    0 = 0 * n

    여기서 n에 어떤 수를 대입해도 성립이 되므로

    n은 어떤 수든 가능합니다.

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    •  
      ALPACA Lv.4 2020.12.17 01:25

      오~ 그런 것이였구요 너무 궁금했었는데 너무 감사드립니다.

      좋아요0
  •  
    유한의끝도못본남자 Lv.7 2021.01.20 22:58

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    나중에 극한이라는 개념을 배우면 알겠지만

    \lim_{x\rightarrow a}f(x)는 x가 a에 완전완전완전 가까워진다고 할때 f(x)의 함숫값입니다

    그렇다면 언제는

    \lim_{x\rightarrow 0}\frac{x}{x}같은 0/0 꼴이 나오는데

     

    이경우 x/x = 1이므로 "극한값(수렴값)"은 1이됩니다 

    하지만

    \lim_{x\rightarrow 0}\frac{x^2}{x}꼴도 0/0꼴이 되는데

    이경우 x^2/x = x이므로

    그대로 0에 가까워지므로 극한값은 0이됩니다

     

    하지만

    \lim_{x\rightarrow 0}\frac{x}{x^n}꼴이라면

    0/0꼴이지만

     

    x/x^n을 정리(약분)하면 1/x^n-1이되는데 이경우 1/0에서 되고

    1/0은 정의되지않지만 0에 아주 가까워지는 것은 단조 증가하지만 1/0은 정의되지않아 상한은 없습니다

    따라서 극한값(발산) = \infty

    입니다 따라서

     

    0/0은 정의 불가능합니다

     

    극한값을 배우면 더 이해가 잘 될 것입니다

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