Lecture 9 (Real Analysis 2020)

A function f : D → ℝ is continuous at x₀ ∈ D provided that whenever (xₙ) is a sequence in D with xₙ → x₀, then:

1. A.f(xₙ) → f(x₀)
2. B.f(xₙ) is bounded
3. C.f(xₙ) is monotone
4. D.xₙ → f(x₀)