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]