- § 337. Historical retrospect
- § 338. Positive doctrine of the infinite
- § 339. Proof that there are infinite classes
- § 340. The paradox of Tristram Shandy
- § 341. A whole and a part may be similar
- § 342. Whole and part and formal implication
- § 343. No immediate predecessor of
`ω`or`a`_{0} - § 344. Difficulty as regards the number of all terms, objects, or propositions
- § 345. Cantor's first proof that there is no greatest number
- § 346. His second proof
- § 347. Every class has more sub-classes than terms
- § 348. But this is impossible in certain cases
- § 349. Resulting contradictions
- § 350. Summary of Part V

The Principles of Mathematics was written by Bertrand Russell, and published in in 1903. It is now available in the Public Domain.