Table of Contents

Axiom and Definitions:

  • Completeness Axiom of R
  • Seq -> Convergent, Cauchy, (bounded) liminf and limsup
  • metric space: open, closed, limit points, closure

Theorems:

  • Convergent <-> cauchy <-> (bounded) so has liminf, limsup
  • limit theorems
  • Bolzano-Weierstrass Theorem
  • Denseness of Q in R
  • I_1 \leq I_2 \leq … \leq liminf \leq limsup \leq … \leq S1