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1) Prove that for all real numbers x and y, if x < y, then x...

1) Prove that for all real numbers x and y, if x < y, then x < (x+y)/2 < y

2) Let a, b ∈ R. Prove that:

a) (Triangle inequality) |a + b| ≤ |a| + |b| (HINT: Use Exercise 2.1.12b and

Proposition 2.1.12, or a proof by cases.)

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