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Full Idea
From the very nature of an irrational number, it seems necessary to understand the mathematical infinite thoroughly before an adequate theory of irrationals is possible. Infinite classes are obvious in the Dedekind Cut, but have logical difficulties
Gist of Idea
Irrationals and the Dedekind Cut implied infinite classes, but they seemed to have logical difficulties
Source
report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite II Intro
Book Ref
Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.11
A Reaction
Almost the whole theory of analysis (calculus) rested on the irrationals, so a theory of the infinite was suddenly (in the 1870s) vital for mathematics. Cantor wasn't just being eccentric or mystical.