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Single Idea 14147

[from 'The Principles of Mathematics' by Bertrand Russell, in 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction ]

Full Idea

The transfinite was obtained by denying mathematical induction.

Gist of Idea

Denying mathematical induction gave us the transfinite

Source

Bertrand Russell (The Principles of Mathematics [1903], §310)

Book Reference

Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.332


A Reaction

This refers to the work of Dedekind and Cantor. This raises the question (about which thinkers have ceased to care, it seems), of whether it is rational to deny mathematical induction.