Chapter 1: Limits and sequences

1. Limits of Sequences
   • Definition, examples
   • Limits are unique
   • Sandwich theorem
   • Arithmetic
2. Bounded sets
   • Upper and lower bounds
   • Suprema and infina
   • Least upper bound property
   • Archimidean property
   • The rationals are dense
3. Monotone sequences
4. Subsequences
   • Definition, examples
   • Bolzano-Weierstrass theorem
5. Cauchy sequences
6. Convergence to infinity and extended real numbers
7. Limsup and liminf