Has anyone tried to start off with irrational numbers as a foundation, then derive the rational numbers from them?
It's an interesting fact CB.
Historically speaking the discovery of the rational numbers preceded the irrational numbers (a secret society was said to have killed someone who revealed the discovery of an irrational number or numbers as that cult feared that the harmony of the rationals would be disrupted). It would seem illogical that the reverse can happen, but to my knowledge nothing has been said about this so I'm exploring this area to see what someone knows about this.