Recounting the Rationals

Recently I found the paper Recounting the Rationals via Mark Jason Dominus on Planet Haskell.

Mark suggests that the paper is a good first paper to read. Well since I am part way through my first Discrete Maths subject, I thought I would give it a go as my first mathematical paper to have a look at.

I was quite suprised that I could actually understand a fair bit of the paper as I read through it. It was interesting just how many of the concepts from my one Uni subject are brought together in this paper: rational numbers, sequences, trees, proof by contradiction, proof by induction and the notion of relatively prime.

I still need to spend some more time to finish exploring this paper and Brent Yorgey's six-part blog series about it. However a couple observations so far:

• The sequence of rationals shown in the paper is quite elegant and fascinating.


• The fact that the sequence can be represented as a tree is even more interesting.


• Starting with sequences, switching to a tree perspective, doing a number of proofs on the tree and then relating the tree back to the sequences was a pretty cool technique.

So my verdict from the experience, is that it has been a good first paper to read. It is only 3 pages long. I could understand the paper at a high-level to start with and it has been interesting and challenging to explore in detail.