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.  

It is indeed unconventional to use vectors in this way.  I think it's safe to say that if you want to do something like check for an "element of a vector", you should invent the appropriate notation (perhaps by overloading the set-theoretic $\in$) and explain what you mean.
