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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.2012-08-23
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    Suppose I am the offspring of blasphemous computer scientists who never write $(s_k)$? :)2012-08-23
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    Are "words" not acceptable? I'd say that $x$ appears in $S$.2012-08-23
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    Parents know best: ask them. I even wrote a few papers in theoretical computer science, but used conventional mathematical notation. There was no apparent outrage.2012-08-23
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    Would something like $\exists i: S_i=x$ be acceptable?2012-08-23
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    @Thomas: I'm not sure I get the point about never writing $(s_k)$. Though I'm not a computer scientist, I wouldn't either, but I would freely write $S=(s_k)_{k\in\mathbf N}$.2012-08-23
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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 $x\in\operatorname{ran}S$.2012-08-23
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    Okay... I should not have said that some people 'never write $(s_k)$'! I will write it like that, using $S = (s_k)_{k \in \mathbb{N}}$ when necessary.2012-08-23

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Remember that a sequence is just a function $S:\mathbb N \rightarrow X$ (with $X$ usually being $\mathbb R$ or $\mathbb N$).

So the set of members of the sequence is just the image of $S$, which can be written as $S(\mathbb N)$ or sometimes $Im(S)$.

Then $x\in S(\mathbb N)$ is a clear and concise way to describe that $x$ appears in $S$.

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    Or: $\exists n\;(x=S(n)).$2017-05-27
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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.2014-02-04
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    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.2014-02-04
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    While it is a drawback, it can still be beneficial if it makes the text more clear.2018-10-25
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One can use any notation, as long as one introduces it explicitly and chooses it well. A sequence is just an ordered set (and usually an at most countable one), so my advice would be to write "In what follows, I write $x \in S$ to denote that $x$ is an element of the sequence $S$".