### Single Idea 10891

#### [catalogued under 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction]

Full Idea

Defining a set by induction enables us to use the method of proof by induction to establish that all the elements of the set have a certain property.

Gist of Idea

If a set is defined by induction, then proof by induction can be applied to it

Source

José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.3)

Book Reference

Zalabardo,José L.: 'Introduction to the Theory of Logic' [Westview 2000], p.48