A subsequence {xnk}k≥1 of a sequence {xn}n≥1 is an sequence selected from {xn} in order. Specifically the map k↦nk is a strictly increasing map from ℕ to ℕ. If {xn} converges to L, then all its subsequences also converge to L. See Bolzano-Weierstrass Theorem.
1. A function whose domain is a subset of the positive integers and hence whose image set can be listed:
2. The listing of the image set of a subsequence. Hence a subsequence of a string a1a2…an is any listing of the form
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