TITLE: Is there a math function to find an element in a vector?
QUESTION [16 upvotes]: I would like to write mathematically, if possible, the following statement:

Given a vector $x=[1,4,5,3]$ and an integer $j=3$, find the position of $j$ in $x$?

How to write this mathematically? 
If I am looking for the position of the minimum value in $x$, I would achieve this by $\arg\min x$. 
I guess $j^*=\operatorname{arg\,find} (x=j)$ but $\LaTeX$ does not recognize this.

REPLY [2 votes]: Vector dot products do this. If you want the second element of a vector $X$, then $X \cdot \langle0, 1, 0, 0, 0\rangle $will give you that component if $X$ is a five-dimensional vector.