Math symbols on vectors e.g item in, item not in, for all I have a vector s= <1,2,3> and I want to perform various operations on it like these ones: 
check if an item x exists in s,
x not in s,
a for all i in s where i is the item.
What is the correct math symbols for doing this on a vector? This is perhaps an unconventional way of utilizing vectors. Note that set notation can't be used for my application as I am highly dependent on an ordered s.  

Viewing a (coordinate) vector as a map from an index set to the set of reals (or whatever), "$x$ is a component of $s$" is the same as saying that $x$ is in the image of that map ...
And unless you are also doing something really vector-ish with them, I'd prefer to  call $s$ a finite sequence of reals.
