Suppose that * is an associative and commutative binary operation on the set of rational numbers such that
- 0*0=0
- (a+c)*(b+c)=(a*b)+c for all rational numbers a,b,c.
Prove that either
- a*b=max(a,b) for all rational numbers a,b, or
- 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 One incorrect solution was submitted (0 point) and one (incorrect) solution was submitted but later withdrawn.
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