Single Idea 14130

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

Full Idea

Dedekind proves mathematical induction, while Peano regards it as an axiom, ...and Peano's method has the advantage of simplicity, and a clearer separation between the particular and the general propositions of arithmetic.

Gist of Idea

Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer

Source

report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Bertrand Russell - The Principles of Mathematics §241

Book Reference

Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.248