Full Idea
The line of development that finally led to a coherent foundation for the calculus also led to the explicit introduction of completed infinities: each real number is identified with an infinite collection of rationals.
Gist of Idea
Completed infinities resulted from giving foundations to calculus
Source
Penelope Maddy (Naturalism in Mathematics [1997], I.3)
Book Reference
Maddy,Penelope: 'Naturalism in Mathematics' [OUP 2000], p.51
A Reaction
Effectively, completed infinities just are the real numbers.