KnowraBolzano–Weierstrass theoremLinked fromLinked fromThe 16 pages that link to Bolzano–Weierstrass theorem, each with the reason it gives.All 16Broader topic 2Related 11Compared with 3Cauchy criterionCompared with: It guarantees a convergent subsequence, not convergence of the whole sequence.Banach–Alaoglu theoremCompared with: The theorem asserts topological compactness, not necessarily a convergent-subsequence property for arbitrary nets or sequences.Monotone convergence theoremCompared with: It guarantees subsequential convergence without requiring the entire sequence to be monotone.