section_path: Formal definitions/Peano axioms
section_name: Peano axioms
paragraph_text: Peano axioms
  
  The five Peano axioms are the following:
  
  These are not the original axioms published by Peano, but are named in his honor. Some forms of the Peano axioms have 1 in place of 0. In ordinary arithmetic, the successor of x {\displaystyle x} is x + 1 {\displaystyle x+1}.