Full Idea
Unlike the intuitionist, the classical mathematician believes in an actual set that contains all the real numbers.
Gist of Idea
The classical mathematician believes the real numbers form an actual set
Source
A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.6)
Book Reference
George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.170