수학동아 - 폴리매스

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함께 풀고 싶은 문제

창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.

[창의 퍼즐] 극한 허수

코딩하는 중딩 2019.05.31 06:54 조회 590

문제 푼 사람 0명

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

$l(x)$ 를 $x$ 와 무한히 가까운 수라고 정의할 때,

$l(i)$ 는 실수인가?

* 허수는 고등학교 때 배우는 수 체계로, $\sqrt{-1}$ 을 나타내며, 기호 $i$ 로 나타낸다.

이전글 극한 1+1

다음글 재미있는 날

이 문제 어떠셨나요?

글쎄요

어려워요

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c언어 Lv.4 2019.06.01 02:52

x라는 점에 가까워 진다는 것을 |a-x|인 절댓값이 작아진다고 생각하겠습니다. 보통 극한을 상상할때 수직선에서 x라는 점에 점점 가까워 지는 경우를 생가하는데, 이를 더 확장에서 수직선이 아니고 복소평면이라고 한다면 수평선(x축)에 있을경우는 실수가 되고 그 이외의 경우에는 복소수가 됩니다. 그러니까 어떤 수에 가장 가까운 수는 실수도 되고 복소수도 되지 않을까요? 하나로 딱 정해지는 수는 아닌거 같습니다. 즉 실수로 하거나 복소수로 하여도 상관 없는거 같아요.

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- 코딩하는 중딩 Lv.1 2019.06.02 00:11
  
  그것도 좋은 생각 같습니다.
  
  좋아요0
Cantor Lv.3 2019.06.04 00:41

가장 가까운 살수는 0인데도 거리가 1입니다.(복소평면)

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뉴턴의 사과 Lv.1 2019.07.19 19:05

애초에 정의가 좀 애매한것 같네요. x와 무한히 가까운 수라는 건 x가 포함된 공간에서 얘기하는 거겠죠. 그러면 무한히 가까운 수는 뭔가요? real number space의 경우에도 무한히 가까운 수라는 걸 정의하기가 좀 뭐한데...

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