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홍차넷
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Warning: Use of undefined constant is_admin - assumed 'is_admin' (this will throw an Error in a future version of PHP) in /home/redtea/html/zero_header.php on line 269
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추천
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/bbs_title.php on line 21
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- 회원들이 추천해주신 좋은 글들을 따로 모아놓는 공간입니다.
- 추천글은 매주 자문단의 투표로 선정됩니다.
Warning: Use of undefined constant use_formmail - assumed 'use_formmail' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/lib.php on line 519
Warning: Use of undefined constant use_category - assumed 'use_category' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/include/print_category.php on line 9
전체기타일상/생각꿀팁/강좌게임문학영화의료/건강문화/예술경제체육/스포츠과학철학/종교정치/사회요리/음식역사여행IT/컴퓨터음악창작사진
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Warning: Use of undefined constant name - assumed 'name' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 2
Warning: Use of undefined constant HTTP_HOST - assumed 'HTTP_HOST' (this will throw an Error in a future version of PHP) in /home/redtea/html/pb/memo_replace.php on line 3
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| Date |
Warning: Use of undefined constant reg_date - assumed 'reg_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 53 20/07/02 17:07:31 Warning: Use of undefined constant mod_date - assumed 'mod_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 56 수정됨 |
| Name | 캡틴아메리카 |
| Subject | 사칙연산 아니죠, 이칙연산 맞습니다. (부제: 홍차넷 수학강의 시즌2 프롤로그) |
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[수학에 서론 같은 건 없어요. 그저 시작부터 달리는 겁니다.] - 仁碩 Lee 교수님의 가르침을 받은 한 수학빌런의 말 - 여러분은 혹시 학창시절 수학시간에 배운 [항등원], [역원]이라는 개념을 기억하시나요? 항등원, 역원이라는 개념은 2009년 개정 교육과정 이후 고교 수학에서 행렬 파트와 함께 빠지게 되면서 비교적 최근에 고등학교를 졸업한 분들은 배우지 않는 개념입니다. 대수학을 좋아했던 사람으로서 참으로 안타까운 교육과정 개정이었죠... 혹시 배우지 않았거나 기억이 가물가물한 분들을 위해 이것들을 설명하고 넘어가죠. [항등원]은 임의의 "어떤 수"에 [다른 수]를 연산하여도 변함없이 그 "어떤 수"가 유지되게 만드는 그 [다른 수]를 뜻해요. 덧셈(+)으로 예를 들면, 임의의 "어떤 수 a"가 있을 때 a + e = a이고 e + a = a가 되게 하는 그 [다른 수 e]가 바로 항등원이에요. 여러분은 이 때 e가 무엇인지 아시겠나요? 네, 바로 e = 0 입니다. 그렇다면 곱셈(x)으로 생각해보면 항등원이 무엇일까요? 네, 바로 1이 항등원입니다. a x 1 = 1 x a = a니까요. 덧셈이든 곱셈이든 항등원은 "어떤 수 a"가 무엇이 되든 항상 항등원은 0으로 혹은 1로 정해져 있어요. [역원]은 각각의 어떤 수에 [다른 수]를 연산해서 '항등원'이 나오게 하는 그 [다른 수]를 뜻해요. 덧셈(+)을 생각하면, "어떤 수 a"가 있을 때 a + b = 0이고 b + a = 0이 되게 하는 그 [다른 수 b]가 바로 역원이에요. 이 때 b는 무엇인가요? 네, 바로 b = -a 입니다. 곱셈(x)에서도 비슷하게 생각해보면 1/a이 역원이 되죠. a x (1/a) = (1/a) x a = 1이니까요. 덧셈이든 곱셈이든 역원은 "어떤 수 a"가 정해져야 역원이 같이 정해집니다. 덧셈에서 a = 2이면 역원은 b = -2가 되고, a = 10이면 역원은 b = -10이 되죠. 곱셈에서 a = 3이면 역원은 b = 1/3이고, a = 100이면 b = 1/100이 됩니다. "곱셈에서 a = 0의 역원은 어떻게 되나요?" 같은 질문은 받지 않습니다. 곱셈에서 a = 0의 역원은 애초에 정의하지 않기 때문에 대수학에서는 관심대상이 아니거든요. 이 질문은 해석학 하시는 분께 해보시기 바랍니다. :) 그럼 이제 본론으로 들어가보죠. (근데 본론이 더 짧네요. ㅋㅋㅋ) 사람들은 일상생활에서 덧셈(+), 뺄셈(-), 곱셈(x), 나눗셈(/) 이렇게 네 가지의 연산을 주로 사용합니다. 우리는 이것들을 [사칙연산]이라 부르죠. 그런데 뺄셈(-)은 사실은 덧셈에서 역원을 생각하는거에요. 예를 8 - 5 = 3라는 식이 있으면 이것은 사실은 8 + (-5) = 3이라는 식인 거에요. 즉 8에서 "5의 덧셈에 대한 역원"인 -5를 더해서 3이라는 결과가 나오게 되는 것이죠. 나눗셈(/)도 마찬가지에요. 6 / 2 = 3이라면 이것은 6 x (1/2) = 3인 겁니다. 6에서 "2의 곱셈에 대한 역원"인 1/2을 곱해서 3이 나오는 거에요. 사실 연산의 성질을 살펴봐도 덧셈, 곱셈과 뺄셈, 나눗셈은 큰 차이가 있습니다. [결합법칙]이나 [교환법칙]이 바로 그것입니다. (2 + 3) + 4을 하나 2 + (3 + 4)를 하나 결과는 똑같죠. 그래서 우리는 괄호를 생략하고 2 + 3 + 4를 해도 아무 상관이 없습니다. 7 x 8을 하나 8 x 7을 하나 결과는 역시 똑같습니다. 그런데 뺄셈과 나눗셈은 이런 것들이 일반적으로 되지가 않죠. 5 - 3과 3 - 5가 같지 않으며 (72 / 12) / 3과 72 / (12 / 3)이 같지가 않죠. 그래서 뺄셈이나 나눗셈, 특히 나눗셈이 섞인 연산이 나오면 이상한 논란들이 일어나게 되죠. 48÷2(9+3) 같은 것 말입니다. 이에 관한 논의는 아래의 유튜브 영상을 참고하시기 바랍니다. 이 글에서는 더 이야기 하지 않겠습니다. https://www.youtube.com/watch?v=3doWeqpD5gk 그래서 이야기의 결론은 무엇이냐... 우리가 일상생활에서 자주 쓰는 연산은 본질적으로 덧셈과 곱셈 이렇게 두 가지 연산이라는 겁니다. 뺄셈과 나눗셈은 역원의 개념에서 파생되어 온 것이라 보면 되요. 한줄요약: [이 글의 제목] 그리고 저는 이 글의 연장선으로 올여름 홍차넷 수학강의 시즌2를 진행할 생각입니다. - 캡틴아메리카의 [고.조.선.] 수강생 모집 - [고]오급 [조]오낸 까다로운 [선]형+대수학 * 참고: 이 강의는 선형대수학을 배우는 강의가 아닙니다. 혹시나 착각 하실까봐 덧붙입니다. :) 강의은 [7월 9일 부터 매주 목요일 오후 2시 ~ 5시]로 약 3~4주간 진행할 생각입니다. (물론 수강생분들의 일정을 고려하여 변동될 가능성도 있습니다.) 수강생 분들의 반응이 좋고 잘 따라오시면 최대 5주까지도 해 볼 생각입니다. * 이 강의를 듣기 위해 필요한 소양 최소소양: 온라인 화상프로그램 ZOOM을 사용할 줄 아시는 분 (시국이 좋지 않으므로 랜선을 통한 실시간 강의로 진행됩니다.) 권장소양: 스스로 수학적 머리가 좀 된다 하시는 분 우대소양: 선형대수학을 배우신 분 (벡터공간의 정의만 알아도 됨) [댓글로 수강신청 받습니다.] * Cascade님에 의해서 티타임 게시판으로부터 게시물 복사되었습니다 (2020-07-14 01:08) * 관리사유 : 추천게시판으로 복사합니다. Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 133 Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 146 Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view.php on line 161 5 |
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Warning: Use of undefined constant file_name - assumed 'file_name' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 28
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 65
20625 class="iamcmt" style="display:none;"> Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 66
20625 class='vcm '>
Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 70
Warning: Use of undefined constant x - assumed 'x' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 71
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 76
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 117
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 118
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 119
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 120
Warning: Use of undefined constant ismember - assumed 'ismember' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 121
20625'> Cascade
Warning: Use of undefined constant mod_date - assumed 'mod_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 133
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 140
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 140
Warning: Use of undefined constant reg_date - assumed 'reg_date' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 142
20/07/02 17:09
20625>삭제 주소복사
Warning: Use of undefined constant level - assumed 'level' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 150
아 저 이해함
그 게임에서 딜 넣는 거랑 힐 넣는 건 사실 똑같다는 의미죠?
그러니까 딜의 역원 = 힐, 힐의 역원 = 딜
Warning: Use of undefined constant level - assumed 'level' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 158
Warning: Use of undefined constant password - assumed 'password' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 166
Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 171
Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 172
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 173
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 173
Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 173
1
그 게임에서 딜 넣는 거랑 힐 넣는 건 사실 똑같다는 의미죠?
그러니까 딜의 역원 = 힐, 힐의 역원 = 딜
Warning: Use of undefined constant level - assumed 'level' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 158
Warning: Use of undefined constant password - assumed 'password' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 166
Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 171
Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 172
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 173
Warning: Use of undefined constant no - assumed 'no' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 173
Warning: Use of undefined constant vote - assumed 'vote' (this will throw an Error in a future version of PHP) in /home/redtea/html/a_skin/bbsd/view_comment.php on line 173
1
20625>
20625>
