A convergent subsequence of (xn) is a sequence (xnk) with strictly increasing indices nk that converges to a limit.
Ancestors (5)
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- Bernard Bolzano
- Bolzano-Weierstrass theorem
- Brouwer fixed-point theorem
- Cauchy sequence
- Cauchy subsequence
- Compactness from uniformly vanishing sequence tails
- Compact space
- Distance-increasing self-map theorem for sequentially compact metric spaces
- Finite-codimensional weak-star dense dual subspace is norming
- Infinite-dimensional bounded sequences can lack convergent subsequences
- Limit inferior and limit superior
- Minimizing sequence
- Parameter continuity of variational regularization
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- Peano existence theorem
- Product metric
- Schauder fixed-point theorem
- Stationary distribution existence for a finite Markov chain
- Subsequence selection as regular matrix summability
- Topological analysis
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