The power of Cantor's idea of a cardinal number lies in the fact that it is good for classifying and comparing not only finite but also infinite sets with respect to the number of their elements.

Definition: Comparison of Cardinal Numbers

Let \(A\) and \(B\) be sets. We define for the cardinals \(|A|\) and \(|B|\):

Chapters: 1
Definitions: 2
Explanations: 3
Motivations: 4
Proofs: 5 6 7 8 9
Propositions: 10

Thank you to the contributors under CC BY-SA 4.0!




  1. Ebbinghaus, H.-D.: "Einführung in die Mengenlehre", BI Wisschenschaftsverlag, 1994, 3th Edition