How would you go about proving that there is a 1 : 1 correspondence between the set of positive integers and the set of positive rationals.
I know there are a lot of ways to do this but I am looking for one in particular that I learned a few semesters ago. It has something to do with countability and i remember using diagonal lines.
I did some searching through the resources left on my blackboard form the class and found this video. the part i am talking about starts at 2:10 https://www.youtube.com/watch?v=UPA3bwVVzGI
Looking for help or even online resources about how you would write a proof like this out.( maybe not even write the proof but just properly explain it in written form) If anyone has any suggestions I would appreciate it
note: this was listed under a chapter entitled set theory: denumerable, countability and infinity if that is helpful at all.