Chapter 2: Countability and Cardinality

1. Countable and uncountable sets
   • Definition
   • Examples: N, Z, Q, R
   • Countable unions of countable sets are countable
   • Transcendental numbers
2. Cardinality of sets
   • Definitions of |A|≤|B|, |A|≥|B|, and |A|=|B|
   • |A|≤|B| iff |B|≥|A|
   • Axiom of Choice, Zorn's Lemma, Well-Ordering Principle
   • For any A, B, either |A|≤|B| or |B|≤|A|
   • If |A|≤|B| and |B|≤|A| then |A|=|B|