The fifth of Peano's axioms, which states: If a set 
of numbers contains zero and also the successor of every number
in 
,
then every number is in 
.
Induction Axiom
See also
Peano's AxiomsExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Induction Axiom." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/InductionAxiom.html