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: 2017-04-16 11:48:59 | by: *bookofproofs* | references: [581]

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