아무리 찾아봐도 오류가 없는데....

      a와 b가 같은데 a-b는 당연히 0이죠.. 그런데.. (a+b)(a-b)=b(a-b) 에서 양변을 (a-b)로 나눈것이 오류인것 같군요.

      아 정말 그러네요..

      <p>정답은 </p><p>4번째 줄부터 꼬였음... </p>

      수학에서 방정식 해찾다가 2a=a면 당연히 a=0...;;;;으로 했던것 같은데요..<br />끝에서는 정말 a로 나누면 0으로 나누는 꼴..

      <p><table style="WIDTH: 469pt; BORDER-COLLAPSE: collapse" border=0 cellSpacing=0 cellPadding=0 width=625 x:str><colgroup><col style="WIDTH: 119pt; mso-width-source: userset; mso-width-alt: 4522" width=159><col style="WIDTH: 105pt; mso-width-source: userset; mso-width-alt: 3982" width=140><col style="WIDTH: 60pt" width=80><col style="WIDTH: 125pt; mso-width-source: userset; mso-width-alt: 4721" width=166><col style="WIDTH: 60pt" width=80><tbody><tr style="HEIGHT: 13.5pt" height=18><td style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 1pt solid; BACKGROUND-COLOR: transparent; WIDTH: 119pt; HEIGHT: 13.5pt; BORDER-TOP: windowtext 1pt solid; BORDER-RIGHT: windowtext 1pt solid" class=xl26 height=18 width=159><font size=3 face=돋움>문</font></td><td style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; WIDTH: 165pt; BORDER-TOP: windowtext 1pt solid; BORDER-RIGHT: black 1pt solid" class=xl24 width=220 colSpan=2><font size=3 face=돋움>예1. a와b가 0인경우</font></td><td style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; WIDTH: 185pt; BORDER-TOP: windowtext 1pt solid; BORDER-RIGHT: black 1pt solid" class=xl24 width=246 colSpan=2><font size=3 face=돋움>예2. a와b가 1인경우</font></td></tr><tr style="HEIGHT: 13.5pt" height=18><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext 1pt solid; BACKGROUND-COLOR: transparent; HEIGHT: 13.5pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22 height=18><font size=3 face=돋움>　</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>　</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>　</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>　</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>　</font></td></tr><tr style="HEIGHT: 13.5pt" height=18><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext 1pt solid; BACKGROUND-COLOR: transparent; HEIGHT: 13.5pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22 height=18><font size=3 face=돋움>a=b</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>0=0</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>ok</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>1=1</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>ok</font></td></tr><tr style="HEIGHT: 13.5pt" height=18><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext 1pt solid; BACKGROUND-COLOR: transparent; HEIGHT: 13.5pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22 height=18><font size=3 face=돋움>a²=ab</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>0²=0x0</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>ok</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>1²=1x1</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>ok</font></td></tr><tr style="HEIGHT: 13.5pt" height=18><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext 1pt solid; BACKGROUND-COLOR: transparent; HEIGHT: 13.5pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22 height=18><font size=3><font face=돋움>a²-b<font class=font6><b>²</b></font><font class=font0>=ab-b²</font></font></font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>0²-0²=(0x0)-0²</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>ok</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>1²-1²=(1x1)-1²</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>ok</font></td></tr><tr style="HEIGHT: 13.5pt" height=18><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext 1pt solid; BACKGROUND-COLOR: transparent; HEIGHT: 13.5pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22 height=18><font size=3 face=돋움>(a+b)(a-b)=b(a-b)</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>(0+0)(0-0)=0(0-0)</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>ok</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>(1+1)(1-1)=1(1-1)</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>ok</font></td></tr><tr style="HEIGHT: 13.5pt" height=18><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext 1pt solid; BACKGROUND-COLOR: transparent; HEIGHT: 13.5pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22 height=18><font size=3 face=돋움>(a+b)=b</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>(0+0)=0</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>ok</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>(1+1)=1</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>no</font></td></tr><tr style="HEIGHT: 13.5pt" height=18><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext 1pt solid; BACKGROUND-COLOR: transparent; HEIGHT: 13.5pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22 height=18><font size=3 face=돋움>a+a=a</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>0+0=0</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>ok</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>1+1=1</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>no</font></td></tr><tr style="HEIGHT: 13.5pt" height=18><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext 1pt solid; BACKGROUND-COLOR: transparent; HEIGHT: 13.5pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22 height=18><font size=3 face=돋움>2a=a</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>2x0=0</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>ok</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>2x1=1</font></td><td style="BORDER-BOTTOM: #ece9d8; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl22><font size=3 face=돋움>no</font></td></tr><tr style="HEIGHT: 14.25pt" height=19><td style="BORDER-BOTTOM: windowtext 1pt solid; BORDER-LEFT: windowtext 1pt solid; BACKGROUND-COLOR: transparent; HEIGHT: 14.25pt; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl23 height=19><font size=3 face=돋움>2=1</font></td><td style="BORDER-BOTTOM: windowtext 1pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl23><font size=3 face=돋움>2=1 (2=1이 아니다)</font></td><td style="BORDER-BOTTOM: windowtext 1pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl23><font size=3 face=돋움>no</font></td><td style="BORDER-BOTTOM: windowtext 1pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl23><font size=3 face=돋움>2=1</font></td><td style="BORDER-BOTTOM: windowtext 1pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: transparent; BORDER-TOP: #ece9d8; BORDER-RIGHT: windowtext 1pt solid" class=xl23><font size=3 face=돋움>no</font></td></tr></tbody></table></p>

      [!--18970|1--] <p>심마니아님과 마더론님이 정답인것같습니다....</p><p>위의 그림은 4번째 단계에서 마더론님같이 올바르게 풀이를 하지 않고 common denominator 인 (a-b)를 양변에서 나눠버린것 때문에,</p><p>(A+B)=B 라는 잘못된 단계로 넘어간것같이 보이네요... </p><p>고로, 4번째 단계에서 잘못 풀이가 되어, 5번째에서부터 나머지 윗부분의 공식들과는 맞지 않게 풀이가 시작이 되는군요...</p>

      [!--18968|1--] <p>2a = a 이면 a = 0 이죠....<br />그런데 저 수식은 2 = 1 이다를 표현하기 위해 2a = a 를 유도해낸것이죠.....</p><p>근원적인것은...<br />모든수는 같다 라는 명제를 장난으로 증명하는 놀이 중 하나로...<br />위의 경우는 2 = 1 이다 라는것을 보여준것입니다....</p><p>임의의 수 a, b 를 가정하고<br />a - b = c</p><p>양변에 a - b 를 곱하면<br />(a - b)(a - b) = c(a - b)<br />전개하면<br />a^2 -2ab + b^2 = ac - bc</p><p>양변에 ab 를 더해주면<br />a^2 -ab + b^2 = ab + ac - bc</p><p>좌변의 b^2 과 우변의 ac를 이항하면<br />a^2 -ab - ac = ab - b^2 - bc</p><p>a(a - b - c) = b(a - b - c)</p><p>양변을 (a - b - c) 로 나누면</p><p><font color=#fe1100>a = b<br /></font><br />어떻게 보면 디바이드 바이 제로의 허구성을 잘 보여주는 일례라고 볼 수 있는데.....<br />이러한 일반적인 경우에서는 디바이드 바이 제로의 오류는 오류라고 지적되는데....<br />상대성이론에서의 디바이드 바이 제로의 오류는 타임머신으로 둔갑하는 경향이 있습니다.......</p>

      수학에서는 0으로 나누는 경우는 정의하지 않습니다.<br />저 식(양변을 a-b로 나누는 과정)이 성립하기 위해서는 "a-b=0이 아닌 수"라는 조건이 전제되어 있야겠죠...^^

      이 게시글과 리플이 저에게는 미스테리군요......<div>어쩌면 공포일지도 ㅎㅎ</div>

      그래서 정답이 a=b=0  이 아니라면, a=b=무한대가 되어야 하지 않을까요?

      흠..딴건 모르겠고 바지가 오류네요 ㅎ<br /><br />배바지처럼  밑위가 너무 길군요 ㅎ