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If we have a sequence (an ordered list)

$$ S=(s_0,s_1,...,s_n). $$

What is the notation for expressing that $S'$ is a (ordered) subsequence of $S$?

  • 6
    The indices can be denoted $n_1< n_2; so, $\{ s_{n_i}\}_{i=1}^\infty$.2011-12-14
  • 0
    I'd write $S' \subseteq S$.2011-12-14
  • 1
    @Peteris That's subset notation. Sets are unordered so this fails the "ordered" requirement.2016-09-24
  • 0
    @ApproachingDarknessFish It's definitely an abuse of notation, but there's lots of times people will use $\subset$ to denote "a subset with all the proper structure", e.g., subgroup, subring, subcategory, etc.2017-12-19
  • 0
    This Q about notation was asked here before, but I don't recall the title.2017-12-20
  • 0
    Subsequence is ambiguous. $\{2,~4,~6,~8,~\dots\}$ may or may not be considered a subsequence of $\mathbb N$ because it is discontiguous.2017-12-23

8 Answers 8