Single Idea 17902

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers]

Full Idea

For any set x, we define the 'successor' of x to be the set S(x) = x U {x}.

Gist of Idea

A successor is the union of a set with its singleton


A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)

Book Reference

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.58

A Reaction

This is the Fregean approach to successor, where the Dedekind approach takes 'successor' to be a primitive. Frege 1884:76.