Single Idea 14422

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic]

Full Idea

Given any series which is endless, contains no repetitions, has a beginning, and has no terms that cannot be reached from the beginning in a finite number of steps, we have a set of terms verifying Peano's axioms.

Gist of Idea

Any founded, non-repeating series all reachable in steps will satisfy Peano's axioms

Source

Bertrand Russell (Introduction to Mathematical Philosophy [1919], I)

Book Reference

Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.8