1.11 Infinite Sets

Russell's Paradox [and ZFC optional]

  1. Russell's Paradox

    Exercise 1

    In Russell's Paradox, \(W \) is mathematically well-defined as a set. The question resides with "which well-defined collections are sets?" Russell's Paradox is not relevant when \(W \) is not a set; even Russell himself knew that it was unjustified to assume that \(W \) was a set! ZFC avoided Russell's Paradox by not allowing \(W \) to be a set.
  2. Zermelo-Frankel with Choice axioms (ZFC)

    Exercise 2