A while ago, I chanced upon a light mathematical essay that made the case that algebraics were the next 'logical' step after irrational numbers.
As I remember it, it built up steadily from natural numbers to rational to irrational to algebraics using equations.
Sadly I lost the link. If anyone remembers reading something like this and has a link, I would appreciate it very much.
Thanks!
ps. This was a mathematician(?)'s personal site. There were others essays on Maths too.