4 ms·
I think the correct definition of A + B is A + 0 = A (or A + 1 = Succ(A), if you insist 0∉ℕ) A + Succ(B) = Succ(A) + B
by orthoxerox 2y ago
I think the correct definition of A + B is
A + 0 = A (or A + 1 = Succ(A), if you insist 0∉ℕ)
A + Succ(B) = Succ(A) + B
- necovek 2y agoNot sure what you mean with "correct", because "correct" is an equivalence class of slightly different definitions? Eg. https://en.wikipedia.org/wiki/Peano_axioms https://en.wikipedia.org/wiki/Peano_axioms has, instead of both yours and mine: A + 0 = A A + Succ(B) = Succ(A + B) They would all be proven in the same manner, though some might be slightly stronger in relation to commutation, making some proofs easier off the bat.