HMMT 二月 2008 · TEAM2 赛 · 第 2 题

英文解析

2. [ 10 ] (Freshman’s Dream) Let z denote z z z · · · z with z appearing n times. Proven n nthat ( x ⊕ y ) = x ⊕ y for all x, y ∈ R ∪ {∞} and positive integer n .
   n n
   Solution: Without loss of generality, suppose that x ≤ y , then LHS = min( x, y ) = x =
   n nnx , and RHS = min( x , y ) = min( nx, ny ) = nx .