Notation for extracting the index of an element from a set OK I edited the question. Sorry for the wrong terms.
What is the correct notation such that a specific function maps an element of a specific sequence/list/n-tuple to its index?
I have researched about index sets but it only gives index to a set and not to the element.
Is there a way to draw the notation of the index of the element like in the index sets?

As Arturo points out in the comments, this question is only meaningful for a list (or sequence), and not a set, since sets have no intrinsic order.  A list can be considered as a function $F: \mathbb{N} \rightarrow S$.  The notation you are seeking is simply $F^{-1}$, the inverse of $F$.  For example, $F(x) = x^2$ corresponds to the list $(0, 1, 4, 9, 16, 25, 36, ...)$, and since $F(6) = 36$, we have $F^{-1}(36) = 6$ mapping the element 36 back to position 6. 
