4 ms·
There are many axiom systems for natural numbers. My favorites are 1. Heyting Arithmetic, and 2. In category theory, one can characterise the natural numbers an
by gylterud 2y ago
There are many axiom systems for natural numbers. My favorites are 1. Heyting Arithmetic, and 2. In category theory, one can characterise the natural numbers and the initial algebra of the X |–> X+1. functor.
- Koshkin 2y agoSure, one can, but does it help with anything? Just curious.
- ketralnis 2y agoIt's up to you if you think it's "better" but it's answering the question of whether Peano axioms are the only fundamental structure
- Koshkin 2y agoCategory Theory itself assumes the existence of natural numbers. My point was about whether their futher "axiomatization" via a functor makes it easier to prove theorems or make discoveries.