Interactive visualizations of key theorems and proofs
Proof by Contradiction using Interval Bisection
Understanding topology in ℝ through visualization
Visualizing open coverings and finite subcovers
Well-definedness, totality, and compatibility of order
Lemma 1.3.3: Sequences and their limits
Understanding sequences approaching from below
Finding rational approximations to irrational numbers
Understanding closed sets through accumulation points
Reverse direction: accumulation points imply closed
A visual guide to compactness: open coverings, finite subcovers, and sequential compactness
Probe points and ε-balls to see interior, boundary, and exterior of a set
Probe points with open balls to see adherent, accumulation, and isolated points of a set
Definition 3.4.1: ε–δ visualization for f(x) → y₀ as x → x₀
fₙ(x) = xⁿ converging to f(x) = 0 on (−1,1) vs [−½,½]