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I'm writing something up and I'm just wondering if there's a notation and/or name for the function which maps the elements of a sequence $(a_1, a_2, \dots)$ (or the finite sequence $(a_1, \dots, a_n)$) to the set which contains all of the same elements $\{a_1, a_2, \dots\}$.

I'm fine with just making up a notation, but I feel like this might be something someone has already come up with a standard symbol for, though a quick Google search didn't find me one.

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    If you look at a sequence as $f:\mathbb{N}\rightarrow X$, then it's just the image. – 2017-02-14
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    If you treat a sequence as a function $f\colon \mathbb N \to S$, then what you are looking for is simply the image of $f$, e.g., $\Im (f)$ if you like fancy stuff. – 2017-02-14
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    OK. I didn't think of that. Thanks. If one of you writes that up as an answer I'll accept it. – 2017-02-14
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    Nah, it's too short (I don't need the points). Feel free to write it yourself and accept it. – 2017-02-14
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    I made it a community-wiki answer. – 2017-02-14

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If you look at a sequence as $f:\mathbb{N}\rightarrow X$, then it's just the image.