Understanding the Pattern of Positive Rational Numbers

[abbeyofthelema]

I am asked to list the positive rational numbers in one list so that the pattern of the order is clear and so that all the positive rational numbers would eventually appear on the list. Then I have to explain the pattern and why every positive rational number will eventually be on the list.
I would imagine that I would be creating a set of some sort, but I am confused by the question because initially i'd just list positive rational number {1,2,3,4...} but i know something is missing. Does anyone have a clearer understanding of what the question is trying to ask? Thank you so much

 

[HallsofIvy]

Every rational number is the ratio of two integers. Do this:
List the positive integers along the top of a table, and then down the side of the table. The number where the n- column intersects the m-row represents the rational number n/m. Now, draw a line that zig-zags through the table. One difficulty is that this will get the same number multiple times: 1/2 will be represented as 2/4, 3/6, 4/8, etc. but at least you WILL get every rational number is a specific list.

(I presume the purpose of this is to show that the set of all positive rational numbers is countable so this is enough.)

 

[abbeyofthelema]

perfect

I was just at school and got back and that's exactly what i finally figured out. thank you so much!