Math and science::Analysis::Tao::02. The natual numbers
Tao's 5 axioms for natural numbers1. [...]
The root node.
The increment operation. The only axiomatic operation.
Prevent loops where there are two nodes that increment to the same node.
Prevent a circle loop back to 0 (not covered by 3).
There are no other connected components other than the one containing 0. A stange approach to address this. Tao mentions that this is more of an 'axiom schema' in logic parlance.