Inductive set (axiom of infinity)
Encyclopedia
In the context of the axiom of infinity
, an inductive set (also known as a successor set) is a set
with the property that, for every 
, the successor
of 
is also an element of 
and the set X contains the empty set 
.
More formally, X is inductive if
An example of an inductive set is the set of natural number
s.
Axiom of infinity
In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of infinity is one of the axioms of Zermelo-Fraenkel set theory...
, an inductive set (also known as a successor set) is a set
with the property that, for every , the successorSuccessor
A successor can refer to* Someone who, or something which succeeds or comes after * Successor , an American Thoroughbred racehorseIn history:* The Diadochi, or Successors to Alexander the GreatIn mathematics:...
of is also an element of and the set X contains the empty set .More formally, X is inductive if
An example of an inductive set is the set of natural number
Natural number
In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...
s.