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

Theorem: Every Bounded Real Sequence has a Convergent Subsequence (Bolzano, Weierstrass)

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).

Notes

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

1.Proof: (related to "Every Bounded Real Sequence has a Convergent Subsequence")

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Bibliography (further reading)

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