more from Penelope Maddy

Single Idea 18190

[catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite]

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


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.