Full Idea
'Definitions' of integers as pairs of naturals, rationals as pairs of integers, reals as Cauchy sequences of rationals, and complex numbers as pairs of reals are reductive foundations of various fields.
Gist of Idea
Complex numbers can be defined as reals, which are defined as rationals, then integers, then naturals
Source
Stewart Shapiro (Foundations without Foundationalism [1991], 2.1)
Book Reference
Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.26
A Reaction
On p.30 (bottom) Shapiro objects that in the process of reduction the numbers acquire properties they didn't have before.