CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search In mathematical logic , the Peano axioms , also known as the Dedekind–Peano axioms or the Peano postulates , are a set of axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano . These axioms have been used nearly unchanged in a number of metamathematical investigations, including research into fundamental questions of consistency and completeness of number theory . The need for formalism in arithmetic was not well appreciated until the work of Hermann Grassmann , who showed in the 1860s that many facts in arithmetic could be derived from more basic facts about the successor operation and induction . [ 1 ] In 1881, Charles Sanders Peirce provided an axiomatization of natural-number arithmetic. [ 2 ] In 1888, Richard Dedekind proposed a collection...