DMP 4.7: Cardinality with Applications

Reading

Cardinality is perhaps the most difficult idea in the chapter and will take a little getting used to. Read through Section 7.4, pages 473–484. Some examples will be looked at in lectures.

Videos

Two links to videos by Marcus du Sautoy, mathematician and Simonyi Professor for the Public Understanding of Science at the University of Oxford.

From Zero to Infinity

Presents ideas about infinity and Hilbert's Hotel. It is 14 minutes long and the infinity section starts at about 8 minutes but the numbers section is interesting as well and relevant.

Cantor and the Mathematics of Infinity

A 3-minute video on Cantor's exploration of infinity.

Exercises

• Exercise Set 7.4 Questions 1, 2, 3, 8, 10, 11, 13, 16, 23a, 25, and 26