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Full Idea
It was primarily Dedekind's accomplishment to define the integers, rationals and reals, taking only the system of natural numbers for granted.
Gist of Idea
Dedekind defined the integers, rationals and reals in terms of just the natural numbers
Source
report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by A.George / D.J.Velleman - Philosophies of Mathematics Intro
Book Ref
George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.13