\(
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\newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}}
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\require{physics}
\require{ams}
\require{mathtools}
\)
Math and science::Analysis::Tao::02. The natual numbers
Tao's 5 axioms for natural numbers
1.
[...]The root node.
2. [...]
The increment operation. The only axiomatic operation.
3. [...]
Prevent loops where there are two nodes that increment to the same node.
4. [...]
Prevent a circle loop back to 0 (not covered by 3).
5. [...]
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.
