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Problem 2. For purposes of this problem, assume that we have already shown that the order < on the set Q of rational numbers is well-defined. Let m, n, p and q be natural numbers. A common mistake among schoolchildren (and adults) is to add the rational numbers m and P as follows: q n + q n This method of addition is wrong. However, it has some interesting properties. Prove that this method of addition yields a rational number that is somewhere between m and p (that q is, less than one of them and greater than the other), unless m and :Po are equal (as rational numbers), in which case the result is equal to both of them.

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Formal Mathematical Reasoning Problem
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