Viewing topic: Inductive Set

See sub-topics for Inductive Set ... >> Mathematics >> Mathematical Analysis >> Inductive Set

Highest Rated Sign

No video has been submitted for this term

Nobody has posted a sign yet.

Inductive Set

  • Definition: A set of real numbers is called an inductive set if it has the following two properties: a) The number 1 is in the set. b) For every x in the set, the number x+1 is also in the set.

    Source: Mathematical Analysis, second edition by Tom M. Apostol

  • Example: The set of all real numbers is an inductive set, as well as the set of all positive real numbers. The set of all positive integers is the smallest inductive set.

  • Listed under: Mathematical Analysis, Set Theory

  • There are no comments for this topic.