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2. (8 points) One of our axioms for the real numbers is the following: \text { for all } a, b, c \in \mathbb{R}, a \leq b \text { implies

} a+c \leq b+c x \leq y \text { for all } i=1,2, \ldots, n \text { implies } x_{1}+x_{2}+\cdots+x_{n} \leq y_{1}+y_{2}+\cdots+y_{n} Use this axiom and induction to prove the following more general statement: for any positive integer n and any x1,..., xn, y1,. .. , yn E R,

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