more from Penelope Maddy

### Single Idea 13022

#### [catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V]

Full Idea

If one is interested in analysis then infinite sets are indispensable since even the notion of a real number cannot be developed by means of finite sets alone.

Gist of Idea

Infinite sets are essential for giving an account of the real numbers

Source

Penelope Maddy (Believing the Axioms I [1988], §1.5)

Book Reference

-: 'Journal of Symbolic Logic' [-], p.486

A Reaction

[Maddy is citing Fraenkel, Bar-Hillel and Levy] So Cantor's great breakthrough (Idea 13021) actually follows from the earlier acceptance of the real numbers, so that's where the departure from common sense started.

Related Ideas

Idea 13021
The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics **[Maddy]**

Idea 15931
The iterative conception needs the Axiom of Infinity, to show how far we can iterate **[Lavine]**