applicability: $\mathbb {N, Z, Q, R, C}$

Every bounded real sequence \((a_n)_{n\in\mathbb N}\) has a convergent subsequence \((a_{n_k})_{k\in\mathbb N}\) (i.e. at least one accumulation point).

- The theorem is named after Bernard Bolzano and Karl-Theodor Weierstrass.
- The theorem can be also formulated for general metric spaces.

| | | | | created: 2015-02-28 13:40:52 | modified: 2020-07-11 09:52:21 | by: *bookofproofs* | references: [581]

[581] **Forster Otto**: “Analysis 1, Differential- und Integralrechnung einer Veränderlichen”, Vieweg Studium, 1983