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Single Idea 18096

[from 'Nature and Meaning of Numbers' by Richard Dedekind, in 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic ]

Full Idea

Dedekind's idea is that the set of natural numbers has zero as a member, and also has as a member the successor of each of its members, and it is the smallest set satisfying this condition. It is the intersection of all sets satisfying the condition.

Gist of Idea

Zero is a member, and all successors; numbers are the intersection of sets satisfying this

Source

report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by David Bostock - Philosophy of Mathematics 4.4

Book Reference

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.101