/sci/ - Science & Math

>>11503637
The proof of uniqueness seems correct.
The existence proof is weird. Specifically, I don't really know whatever it is you did.
My suggestion is as follows: set the property [math]P[/math] as [math]x \in \mathbb{N}[/math] is either zero or the successor of some number, and use induction to show every natural number satisfies [math]P[/math].
I know it feels like some sort of cheating to trivialize the base case like that, but it works fine.