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I'm writing some equations dealing with sets and sequences.

I have a sequence $S$ and want to show that $x$ is an element of $S$, however I am hesitant writing $x \in S$ because I don't want to indicate $S$ is a set. I would also prefer not to write 'substring of length one' (e.g. $\hat{x} \subseteq S$, or something to that effect) because x should not be mistaken for a sequence either.

What is the best notation for 'element of a sequence'?

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Conventional is to call the sequence $(s_k)$ and to denote an individual entry by $s_k$. I agree that "element" is not good. –  André Nicolas Aug 23 '12 at 2:36
    
Suppose I am the offspring of blasphemous computer scientists who never write $(s_k)$? :) –  Thomas Aug 23 '12 at 2:39
    
Are "words" not acceptable? I'd say that $x$ appears in $S$. –  Tunococ Aug 23 '12 at 2:44
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Would something like $\exists i: S_i=x$ be acceptable? –  Marc van Leeuwen Aug 23 '12 at 3:15
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If you don’t care about the index and are only interested in the fact that $x$ is a term of $S$, you can take advantage of the fact that a sequence is a function and write $x\in\operatorname{ran}S$. –  Brian M. Scott Aug 23 '12 at 7:23

1 Answer 1

I would suggest to use a notation, say ||S||, for the set interpretation of a sequence S.

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$\|S\|$ is already used for a lot of other things, though, such as norms. –  T. Bongers Feb 4 at 4:15
    
The drawback to introducing a novel notation (or repurposing one that has other meanings) is precisely the need to define the notation for your audience. –  hardmath Feb 4 at 11:43

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