Mathematics · self-study course
Real analysis: limits and rigorous reasoning
Build epsilon proofs and distinguish pointwise convergence, uniform convergence and compactness.
3 lessons24 quiz questionsAdvanced university
Your learning path
- 01
Sequence limits and epsilon proofs
For every ε>0 there exists N such that every n≥N satisfies the error bound.
Advanced university · Notes · 8 questions - 02
Pointwise versus uniform convergence
The cutoff N may depend on both ε and the point x.
Advanced university · Notes · 8 questions - 03
Compactness and continuous functions
In R^n, compactness is equivalent to being closed and bounded.
Advanced university · Notes · 8 questions