◀ ▲ ▶Branches / Analysis / Theorem: Every Bounded Real Sequence has a Convergent Subsequence
applicability: $\mathbb {N, Z, Q, R, C}$
Theorem: Every Bounded Real Sequence has a Convergent Subsequence
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
Table of Contents
Proofs: 1
Mentioned in:
Definitions: 1
Examples: 2
Proofs: 3 4 5 6
Propositions: 7 8
Theorems: 9
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References
Bibliography
 Forster Otto: "Analysis 1, Differential und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983