Solution: 2009-9 min or max

Suppose that * is an associative and commutative binary operation on the set of rational numbers such that 

  1. 0*0=0
  2. (a+c)*(b+c)=(a*b)+c for all rational numbers a,b,c.

Prove that either

  1. a*b=max(a,b) for all rational numbers a,b, or
  2. a*b=min(a,b) for all rational number a,b.

The best solution was submitted by Jaesong Lee (이재송), 전산학과 2005학번. Congratulations!

Check his Solution of Problem 2009-9.

Alternative solutions were submitted by 김치헌 (수리과학과 2006학번, +3), 권상훈 (수리과학과 2006학번, +3), 양해훈 (수리과학과 2008학번, +3), 백형렬 (수리과학과 2003학번, +2), 김일희 & 오성진 (Princeton Univ., Graduate Student). One incorrect solution was submitted (0 point) and one (incorrect) solution was submitted but later withdrawn.

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3 thoughts on “Solution: 2009-9 min or max

  1. S. Oum Post author

    08학번 양해훈 학생의 정보가 적용이 되지 않았네요……

    양해훈씨, 감사합니다. 지금 적용했습니다.

  2. 양해훈

    08학번 양해훈 학생의 정보가 적용이 되지 않았네요……

    양해훈씨, 감사합니다. 지금 적용했습니다.

    맨 위에 리플 남긴 사람 저 아닌데….

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