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HMMT 二月 2008 · TEAM2 赛 · 第 2 题

HMMT February 2008 — TEAM2 Round — Problem 2

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 10 ] (Freshman’s Dream) Let z denote z z z · · · z with z appearing n times. Prove n n n that ( x ⊕ y ) = x ⊕ y for all x, y ∈ R ∪ {∞} and positive integer n .
解析
  1. [ 10 ] (Freshman’s Dream) Let z denote z z z · · · z with z appearing n times. Prove n n n that ( 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 n nx , and RHS = min( x , y ) = min( nx, ny ) = nx .