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:
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
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.
This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.