Completeness of the Reals

Neighborhoods

Open Sets

Closed Sets

Covers

Compact Sets

Heine-Borel Theorem

Heine-Borel Theorem

Accumulation Points

Closed Sets

Bolzano-Weierstrass Theorem

Sequences

Convergence

Increasing and Decreasing

Bounded Monotone Sequence Theorem

Bounded Monotone Sequence Thm

Completeness again

Bounded Monotone --> Complete

Bounded Monotone --> Complete

Bounded Monotone --> Complete

Completeness Equivalences

The Reals

The Reals