The picture below describes a method of listing all positive rational numbers. W

Question

The picture below describes a method of listing all positive rational numbers. We simply follow the indicated path, listing each rational number in the order we hit it. Let us call the resulting sequence an. Thus, a1 = 1, a2 = 2, a3 = 1 / 2, a4 = 1 / 3. What is the first n such that an = 5 / 3? This is not a one-to-one correspondence by omitting all non-reduced fractions. What is the 14 the fraction is this reduced list? Describe a listing of the set of all rational numbers, including negatives and 0.

Explanation / Answer

a) n=26

b) we have a9=2/3 a37=4/6 = 2/3 hence n=9 m=23 n!=m but an=am

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