https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_game/ https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_g... : > In this game, you get own

https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_game/ https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_g... : > In this game, you get own version of the natural numbers, called `mynat`, in an interactive theorem prover called Lean. Your version of the natural numbers satisfies something called the principle of mathematical induction, and a couple of other things too (Peano's axioms). Such axioms are hard-coded in SymPy, SageMath, and Mathematica but not in Lean Mathlib (which is not optimized for performance) If there are an infinite number of unitary transformations (as rotations on a Bloch sphere for example), I find it unlikely that we've yet discovered all of the requisite operators and axioms and coded them into any human CAS that exists in present day.