How do you put fractions into ascending order? - Answers

You can't, but you can put them into an order (not necessarily ascending), thanks to the denumerability of the set of rational numbers.To do so, consider the following chart:1/1 1/2 1/3 1/4 1/5 1/6 1/7 ...2/1 2/2 2/3 2/4 2/5 2/6 2/7 ...3/1 3/2 3/3 3/4 3/5 3/6 3/7 ...4/1 4/2 4/3 4/4 4/5 4/6 4/7 ...5/1 5/2 5/3 5/4 5/5 5/6 5/7 ...6/1 6/2 6/3 6/4 6/5 6/6 6/7 ...And so on ...All we have to do now is start with zero and alternate negative and positive, starting in the upper-left corner and listing each diagonal.The sequence goes:0, 1, -1, 2, -2, 1/2, -1/2, 3, -3, 1, -1, 1/3, -1/3, ...Notice there are some repeats because 1 = 2/2.An easy fix to this problem is to omit the reducable fractions.Voila! We have counted the rationals!