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'?
Best Answer
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 $S$.