Extrapolating from Eliezers line of reasoning you would probably find that although you remember ss0 + ss0 = ssss0, if you try to derive ss0 + ss0 from the peano axioms, you also discover it ends up as sss0, and starting with ss0 + ss0 = ssss0 quickly leads you to a contradiction.
Extrapolating from Eliezers line of reasoning you would probably find that although you remember ss0 + ss0 = ssss0, if you try to derive ss0 + ss0 from the peano axioms, you also discover it ends up as sss0, and starting with ss0 + ss0 = ssss0 quickly leads you to a contradiction.