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.
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2009-9 min or max,
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