Mathematical and Real Analysis
Explore real numbers and limits; continuity and compactness; functions and integration. Concepts and connections are available independently of video coverage.
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Uniform convergence
One index bounds the approximation error at every point of the domain.
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Pointwise convergence
A sequence of functions converges separately at each point, with tolerances allowed to depend on the point.
Riemann integrability
Riemann integrability requires upper and lower sums to approach the same value for bounded functions.
Bolzano–Weierstrass theorem
Every bounded sequence in finite-dimensional Euclidean space has a convergent subsequence.
Cauchy sequences
Terms of a Cauchy sequence eventually become arbitrarily close to each other.
Compactness
A space is compact when every open cover admits a finite subcover.
Knowledge connections
- Pointwise convergence · Related · Map context
- Riemann integrability · Related · Map context
- Pointwise convergence · Prerequisite · Map context