Math teachers should realize they think they know more than they do. We all do. Students do, teachers do, profs and textbook writers. This is why we need homework and tests to remind us we don’t know as much as we think.
My books on Peano Axioms have more simple examples on the Peano Axioms then exist in other materials combined. (A little self esteem bias there.)
Unfortunately, it may be true. This is because textbook writers and university math webpages underestimate the difficulty and hand holding needed to learn the Peano Axioms and apply them to addition of whole numbers.
That is why my books contain so many examples, solved problems and other problems on the very start of Peano Axioms. These will teach you the 5 rules for counting by one, ie the Peano Axioms and how to apply them.