The Peano axioms

This set of flashcards is optional, for two reasons. (1) Some people may not want to memorize the statements of the individual Peano axioms since it's a lot of extra work, and looking them up as needed is sufficient for getting through the book. (2) The number and ordering of the Peano axioms differs depending on the text. There is no generally-agreed-upon choice of what e.g. the fourth Peano axiom should be. Some books use one axiom and other books use a different one. But to memorize a list, it is important to give an ordering, even if it is arbitrary. Thus we will be unapologetic below in referring to certain axioms as e.g. the fourth Peano axiom. But you have to keep in mind that someone who studied out of a different book will have a different statement in mind if you talk about "the fourth Peano axiom". Since this kind of translation work adds some overhead, some readers may wish to skip it.