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.