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Subsequence preorder

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Sequences are preordered by the subsequence relation. The unique bottom element is the empty sequence. The equivalence class of top elements are those sequences which contain all integers infinitely often, for example:

(Sets are cofinal in this preorder precisely if they contain a top element.) See also Sequences that contain every finite sequence in the Index.

Consequently the relation is a directed preorder.

This preorder has infinite antichains such as {(0, 0, 0, ...), (1, 1, 1, ...), (2, 2, 2, ...), ...}, and hence is not well-quasi-ordered.

Cite this page as

Charles R Greathouse IV, Subsequence preorder. — From the On-Line Encyclopedia of Integer Sequences® (OEIS®) wiki. (Available at https://oeis.org/wiki/Subsequence_preorder)