Bolzano–Weierstrass Theorem
A proof that every bounded sequence in finite-dimensional Euclidean space has a convergent subsequence, with the compactness distinction.
Category
Analysis
4 articles.
2022-04-24
Monotone Convergence Theorem
The monotone convergence theorem for real sequences, proved from the least-upper-bound property and illustrated with examples.
Nested Interval Theorem
The nested interval theorem: completeness gives a common point, while shrinking interval lengths make it unique.
Analysis Foundations: Metric Spaces, Order, and Limits
A grouped reference to algebraic, metric, order, completeness, and limit concepts used across introductory analysis.