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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?

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Sets don't have order; $\{1,2\}$ is the same thing as $\{2,1\}$, so there is no such thing as "its index in the set". If you have an ordered tuple, there is no specific notation for it. – Arturo Magidin Apr 26 '12 at 5:05

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.

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