When I read about Peano axioms I mentally think of Sn as the function S(n) = n+1 and that helps me understand them better. As a non mathematician sometimes I w

When I read about Peano axioms I mentally think of Sn as the function S(n) = n+1 and that helps me understand them better. As a non mathematician sometimes I wonder if this substitution is causing me to misunderstand something else about them.