The sentence is in section 1.5.1 "Minimizing the misclassification rate" (page 39), underlined in red:

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The author thinks this statement is "clear", but I just can't understand. Can you please help me understand it, preferably in rigorous math derivation? Thank you.

  • $\begingroup$ Consider this game: You get to choose one of two numbers. You win when you choose the smaller. Which do you choose? Play this game for each $x$ in turn. That's all this amounts to. $\endgroup$
    – whuber
    Nov 18 at 15:01

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