Single Idea 15918

[catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity]

Full Idea

The paradox of the largest cardinal ('Cantor's Paradox') says the diagonal argument shows there is no largest cardinal, but the class of all individuals (including the classes) must be the largest cardinal number.

Gist of Idea

Paradox: there is no largest cardinal, but the class of everything seems to be the largest

Source

Shaughan Lavine (Understanding the Infinite [1994], III.5)

Book Reference

Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.62


Related Ideas

Idea 15917 Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal [Lavine]

Idea 11015 Cantor's diagonal argument proved you can't list all decimal numbers between 0 and 1 [Cantor, by Read]